DEV Community: maxwizard01

How to group large data into classes using R

maxwizard01 — Sat, 05 Apr 2025 01:15:35 +0000

How to create table for group Data

most of the time as a statisticians or analyst you will be dealing with big data
which might make you need grouping for a convenient view of your data. Imagine your data was given like below.
Example
the following shows the wages of employee in a month.
88,82,96,102,104,106,104,24,26,29,86,36,60,23,24,39,48,46,
33,36,39,78,67,82,32,67,27,24,26,27,30,36,37,49,50,56,83,
99,68,28,55,54,26,29,30,40,46,44,99,84,36,51,86,88,87,29,
40,40,40,66,45,23,26,46,46,96,99,100,100,101,103,106,107,
46,48,49,48,94,55,56,59,60,70,72,76,79,80,50,49,93,86,54,
83,89,90,94,96,99,102,46

as you can see this data is so large that it is hard to say anything about it,
to summarized the data we need table but here we don't just need a frequency table, frequency table could have been nice for it if the data has small range and repeating it self so many times.

what do I need to do when there large range and the element of the data hardly repeat itself??

All you need to do is to group the data in to class by creating some intervals.
it is always advisable to contrust up to 5classes and not more than 15classes.
also each class should have the same class-width.

what is class width??

A class with is just the number of element/value that could possibly be in a class.
for example if a class has the range 21-25 and 20-29 we would say their classwidth is 5 and 10 respectively. that happen because the element that could be consider to be in each class is below.
21-25 : 21,22,23,24 and 25 (5 numbers)
20-29 : 20, 21,22,23,24,25,26,27,28 and 29 (10numbers).

what is the trick to quickly get the classwidth of any class??
the trick I ususlly used is just by finding the range of the class and add 1.
i.e class-width=Range-1
so, for 21-25 ==>Range=25-21 = 4, class-width=4+1 =5.

Now if you look at the data above how do you think we should group them??well this is very easy even if your data is as large as hundreds, thousanads even millions.

How to group my large data set in to Class

To group your data set it is important to know the minimum and maximum value of you data, so as to know where the class should start and end and how large your class width should be.

How to calculate the min and maximum value of data set.

To calculate the minimum and maximum value here make use of the min() and max() functions. for example let us find the maximum and minimum value of the data above. we will write the following codes to do that.

myData=c(88,82,96,102,104,106,104,24,26,29,86,36,60,23,24,39,48,46,
  33,36,39,78,67,82,32,67,27,24,26,27,30,36,37,49,50,56,83,
  99,68,28,55,54,26,29,30,40,46,44,99,84,36,51,86,88,87,29,
  40,40,40,66,45,23,26,46,46,96,99,100,100,101,103,106,107,
  46,48,49,48,94,55,56,59,60,70,72,76,79,80,50,49,93,86,54,
  83,89,90,94,96,99,102,46)
min(data)
max(data)

Result>>

23
107

the codes above shows that the minimum value is 23 and the max value is 107.
Now to group this data we can start from 21 and end at 110 since between this range is all our data set will fall. another question will be "what should we use as our class width?", that one you can picture it yourself. you can decided to use 10 or 15. any of the two is okay but here I will be using 15.
Note: you can use any class with it depend on how large the rang of your data set just make sure you group them into 5 to 15classes.

my classes here will look like the following:
21-35,36-50,51-65...95-110.
if you choose 10 as class width your classes will look like
21-30,31-40,41-50....101-110. this seems much more easy.
we can go on and count the number of observation fall in each class and write it as the respective frequency for each class.

How do I Group my data set using R.

I believed you already understand the theoretical way to construct the data now let us see how to do it using code.
Before we write the codes, u should know the following important functions.

seq(): it is used to form a sequence of numbers, it takes three important argument;from,to and by. i.e the start,end and increment.
cut(): the function used to divide large data set into classes by stating the upper class limit of each class in a sequence. it takes 3important argument; data, break, label and include.lowest.
table(): to tabulate any data set given or represent it in a tabular form.

Now let's make use of the above functions to solve the problem.
Codes>>>

myData=c(88,82,96,102,104,106,104,24,26,29,86,36,60,23,24,39,48,46,
  33,36,39,78,67,82,32,67,27,24,26,27,30,36,37,49,50,56,83,
  99,68,28,55,54,26,29,30,40,46,44,99,84,36,51,86,88,87,29,
  40,40,40,66,45,23,26,46,46,96,99,100,100,101,103,106,107,
  46,48,49,48,94,55,56,59,60,70,72,76,79,80,50,49,93,86,54,
  83,89,90,94,96,99,102,46)
groupData=cut(myData,break=seq(20,110,15),include.lowerclass=FALSE)
table(groupData)

Result>>

 (20,35]  (35,50]  (50,65]  (65,80]  (80,95] (95,110] 
    19       27       10       10       16       18

the result above shows each class and their respective frequency using class width of 15.

How does the Codes work??

One particular thing I usually emphasis on is "understand how the codes work if you want codes to work for you". so I will explain more on how the parameters for cut() function works.
first parameter is the data-set, second is break this is used to show how we want to break the class. since I already know the where my class will start and end together with the class width, then it will be nice to use seq() function to show the breaking point for each class.

the third parameters could be set to true or false, but I use False here because I know I am not going to include 20 in the first class, remember my target is between 21 and 110.

The result above is telling you that 19 of the data fall between 21 and 35. Note that ( mean greater than and ] means less than or equal to .
i.e (21,35] means datas greater than 20 and less than or equal to 35 which is the same thing as to say 21-35.
is there a way to write those classes in our own better ways??
Of course yes! you can write each class in a better way so that you don't need to understand the bracket. take a look at the following codes


myData=c(88,82,96,102,104,106,104,24,26,29,86,36,60,23,24,39,48,46,
  33,36,39,78,67,82,32,67,27,24,26,27,30,36,37,49,50,56,83,
  99,68,28,55,54,26,29,30,40,46,44,99,84,36,51,86,88,87,29,
  40,40,40,66,45,23,26,46,46,96,99,100,100,101,103,106,107,
  46,48,49,48,94,55,56,59,60,70,72,76,79,80,50,49,93,86,54,
  83,89,90,94,96,99,102,46)
lowerclass=seq(21,110,15)
upperclass=lowerclass+14
classInterval=paste(lowerclass,'-',upperclass)
groupData=cut(myData,breaks=seq(20,110,15),
labels=classInterval,include.lowerclass=FALSE)
table(groupData)

Result>>

21 - 35 36 - 50 51 - 65 66 - 80 81 - 95 96 - 110
19 27 10 10 16 18

How the codes work
if you try to run seq(21,110,15) you will realized that this gives you exactly the lower class limit for each class. you should be careful here as what we wanna deal with here is exactly how to write it in our natural ways instead of using bracket.
so, to get the upper class we know we need to add the class width but remember you must subtract 1.
Now we can definitely match both together to form the range. paste() is the function used here to deal with that task. then I add labels to the cut() parameters letting it equal to the classInterval I just created. and boom! we did it.

This is quite interesting! but if you are someone like me I will like it if the table is two column table and how do I do that?? very easy, just make use of Dataframe() function and you are done. take a look at the following codes.

Codes>>

  myData=c(88,82,96,102,104,106,104,24,26,29,86,36,60,23,24,39,48,46,
  33,36,39,78,67,82,32,67,27,24,26,27,30,36,37,49,50,56,83,
  99,68,28,55,54,26,29,30,40,46,44,99,84,36,51,86,88,87,29,
  40,40,40,66,45,23,26,46,46,96,99,100,100,101,103,106,107,
  46,48,49,48,94,55,56,59,60,70,72,76,79,80,50,49,93,86,54,
  83,89,90,94,96,99,102,46)
lowerclass=seq(21,110,15)
upperclass=lowerclass+14
classInterval=paste(lowerclass,'-',upperclass)
wages=cut(myData,breaks=seq(20,110,15),
                    labels=classInterval,include.lowerclass=FALSE)
groupTable=table(wages)
data.frame(groupTable)

Result>>

    wages    Freq
1   21 - 35   19
2   36 - 50   27
3   51 - 65   10
4   66 - 80   10
5   81 - 95   16
6  96 - 110   18

This is incredible right?? I hope you enjoy this article?? if yes then don't forget to share it to some else who might interested. you can drop me a comment.

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How to construct frequency polygon graph in R programming.

maxwizard01 — Wed, 13 Apr 2022 13:28:44 +0000

Frequency Polygons

A frequency polygon is a graph that is obtained by joining the class marks of a histogram with the two end points lying on the horizontal axis. It gives an idea of the shape of the distribution. It can be superimposed on the histogram by placing the dots on the class marks of the histogram, as shown below.

You probably have learned how to do this in college. However won't it be nice if we can have something That could do that for us especially when we have large data??? Who doesn't want that😆🤪🤪???. Alright keep reading.

steps to take to plot frequency polygon.

Get your data and plot histogram using hist() function and provide necessary parameters.
get the vector of the mid-point of all the bars.
Get the vector of all the breaking point of your data
Draw a line using lines() function such that the vector in number2 be on y axis and vector in number3 be on x-axis.
Make any adjustments if necessary.

Construction of histogram using R

Here we going to make use of the following example, so we need to plot histogram first.

Example1

Use the following data showing the score of 50 students to construct frequency polygon.
22 17 26 27 14 15 21 18 8 19 26 14 20 12 11 17 20 16
26 12 21 15 18 21 10 16 20 18 21 22 21 15 19 10 25 15
16 31 24 21 14 24 23 20 14 15 16 29 20 21.

Solution
step1: input all the data and plot the histogram.

codes>>

score=c(22, 17, 26, 27, 14, 15 ,21, 18 , 8, 
        19, 26, 14, 20, 12, 11 ,17, 20, 16,26, 12,
        21 ,15, 18, 21, 10, 16 ,20, 18 ,21, 22, 21, 
        15, 19, 10, 25 ,15,16, 31, 24, 21, 14, 24, 
        23, 20 ,14, 15 ,16, 29, 20, 21)

hist.score=hist(score,main='Histogram of the scores',
       breaks =8,col = 'lightblue',border = 'red')

Result>>

Now let's see some information about our histogram, notice that the histogram was assigned to a particular variable.
codes>>

score=c(22, 17, 26, 27, 14, 15 ,21, 18 , 8, 
        19, 26, 14, 20, 12, 11 ,17, 20, 16,26, 12,
        21 ,15, 18, 21, 10, 16 ,20, 18 ,21, 22, 21, 
        15, 19, 10, 25 ,15,16, 31, 24, 21, 14, 24, 
        23, 20 ,14, 15 ,16, 29, 20, 21)

hist.score=hist(score,main='Histogram of the scores',
       breaks =8,col = 'lightblue',border = 'red')
hist.score

Result>>

$breaks
[1]  5 10 15 20 25 30 35

$counts
[1]  3 12 16 13  5  1

$density
[1] 0.012 0.048 0.064 0.052 0.020 0.004

$mids
[1]  7.5 12.5 17.5 22.5 27.5 32.5

$xname
[1] "score"

$equidist
[1] TRUE

attr(,"class")
[1] "histogram"

As you can see above the breaks tell us exactly all breaking point of our bars. mids is telling us all the midpoint while counts is giving us the frequency of each bars. now we can use those information to draw the frequency polygon line by listing the vector of x-axis and y-axis. see the following codes;

codes>>

score=c(22, 17, 26, 27, 14, 15 ,21, 18 , 8, 
        19, 26, 14, 20, 12, 11 ,17, 20, 16,26, 12,
        21 ,15, 18, 21, 10, 16 ,20, 18 ,21, 22, 21, 
        15, 19, 10, 25 ,15,16, 31, 24, 21, 14, 24, 
        23, 20 ,14, 15 ,16, 29, 20, 21)

hist.score=hist(score,main='Histogram of the scores',
       breaks =8,col = 'lightblue',border = 'red')
xaxis=c(min(hist.score$breaks),hist.score$mids,max(hist.score$breaks))
y.axis=c(0,g$counts,0)
lines(x.axis,y.axis,type='l')

Result>>

Now we have constructed the polygon right? Well, you might not like it this, why?? You may be someone like me who want the polygon without the histogram. so to do that all you have to do is to change the color and the border of the histogram to transparent like the following;
Codes>>

score=c(22, 17, 26, 27, 14, 15 ,21, 18 , 8, 
        19, 26, 14, 20, 12, 11 ,17, 20, 16,26, 12,
        21 ,15, 18, 21, 10, 16 ,20, 18 ,21, 22, 21, 
        15, 19, 10, 25 ,15,16, 31, 24, 21, 14, 24, 
        23, 20 ,14, 15 ,16, 29, 20, 21)

hist.score=hist(score,main='Histogram of the scores',
       breaks =8,col = 'transparent',border = 'transparent')
xaxis=c(min(hist.score$breaks),hist.score$mids,max(hist.score$breaks))
y.axis=c(0,g$counts,0)
lines(x.axis,y.axis,type='l')

Example 2

Use the following data showing the score of 100 students in a statistics exam to construct frequency polygon.
Codes>>

examScores=scan()
63 60 57 55 60 56 58 61 62 60 60 60 58 60 59 60 60 60 58 62 58 63 60 62 61
61 58 59 61 61 61 61 59 61 61 57 58 57 62 59 60 59 59 57 58 58 62 59 58 60
64 59 60 57 60 61 62 61 61 61 60 57 57 58 60 56 58 65 63 63 58 61 60 59 60
60 61 61 59 57 58 57 58 56 60 58 60 58 58 56 64 57 61 57 57 59 57 63 60 61

hist.Score=hist(examScores,main='Histogram of the scores',
       breaks =8,col = 'lightblue',border = 'red')
x.axis=c(min(hist.Score$breaks),hist.Score$mids,max(hist.Score$breaks))
y.axis=c(0,hist.Score$counts,0)
lines(x.axis,y.axis,type='l')

Result>>

you may remove the histogram part using the same method like the following;
Codes

examScores=scan()
63 60 57 55 60 56 58 61 62 60 60 60 58 60 59 60 60 60 58 62 58 63 60 62 61
61 58 59 61 61 61 61 59 61 61 57 58 57 62 59 60 59 59 57 58 58 62 59 58 60
64 59 60 57 60 61 62 61 61 61 60 57 57 58 60 56 58 65 63 63 58 61 60 59 60
60 61 61 59 57 58 57 58 56 60 58 60 58 58 56 64 57 61 57 57 59 57 63 60 61

hist.Score=hist(examScores,main='Histogram of the scores',
       breaks =8,col = 'transparent',border = 'transparent')
x.axis=c(min(hist.Score$breaks),hist.Score$mids,max(hist.Score$breaks))
y.axis=c(0,hist.Score$counts,0)
lines(x.axis,y.axis,type='l')

Result>>

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How I build my own calculator that group any data set given in to classes using R.

maxwizard01 — Sat, 02 Apr 2022 12:28:06 +0000

How I build my own calculator that group any data set given in to classes using R.

I can vividly remember when I was in college, There was one of our lecturer who liked to keep us busy with too much assignments. there was a time we were given 20 different data sets. they are large ones and the question is to group each of them and calculate some necessary statistical value for each.

I must say I was a little lazy boy then, I just don't like repeating something and stressing myself when I already understand the basic. so I thought through the way to make it faster, But I couldn't see any better way. luckily, it comes to my mind that I should be able to build calculator that could do this for me. that was how I got the idea. lol.

How to group large data set into classes and calculate all important statistical value

Firstly let me say if you don't know how to group data set before kindly click here so that my codes doesn't look like magic. But before I showed you the codes let me explain the step taken to arrive at my simple project.

steps taken to create a calculator that group large data set in to classes and also calculate some statistical value showing important workings

Step1: I need a codes to group the data in to classes with any given class width to form a group frequency table.

step2: I need to calculate the class boundary; this is done by subtracting 0.5 from lower limit and adding 0.5 to upper class limit of each class.

step3: I need to write codes that will calculate the class mark; this is the mid point of each class.

Step4: I need codes to find the multiplication of each class mark with respective frequency.

Step5: I need codes to calculate the mean using summation of Fx divided by summation of the frequency

Step6: I need codes to get me the deviation and its squared.

step7: I have to calculate the variance and standard deviation using the formula.

As you can see above the problem I want my calculator to for me was listed above. I will start picking the step one by one.

How to write a codes that group any data set in to classes using the given width.

I will be writing codes in form of function as i want a reusable codes so everything will be inside function so that I can always call the function when needed. Before the codes if you have no knowledge on how to group data before click here to read my article on as there are much things to explain here so I won't explain much on it. take a look at the following codes

Codes>>

reateGroupTable=function(data,classwidth){ 
minimumValue=(min(data)%/%classwidth)*classwidth # to calculate a value less than the minimum value in the data set.
MaximumValue=((max(data)%/%classwidth)+1)*classwidth
d=MaximumValue+classwidth #to get the last upper class limit
lowerclass=seq(minimumValue,MaximumValue,classwidth) # to get a sequence of all lower class limit.
upperclass=lowerclass+classwidth-1 #to form a sequence of all upperclass limit.
classInterval=paste(lowerclass,'-',upperclass) # the sequence of the labels for each class.
alldata=table(cut(data,seq(minimumValue-1,d-1,classwidth), labels=classInterval)) # to tabulate the data
mytable=data.frame(alldata) # turn the table to two column 
mytable
}

The codes above is just a function and when you run it it gives no output since the function has not been executed. So let us try the following data to test it.

Example.

Construct a group frequency table for the following score of 30students.
24, 46, 16, 33, 16, 13, 28, 19, 47, 49, 8, 56, 20, 26, 28, 29, 30, 18, 19, 15, 47, 32, 14, 25, 14, 16, 23, 12, 14, 13

14, 16, 16, 13, 16, 13, 18, 19, 7, 9, 8, 6, 20, 26, 28, 29, 30, 18, 19, 15, 17, 12, 14, 15, 14, 16, 13, 12, 14, 13.

Codes>>>

createGroupTable=function(data,classwidth){ 
minimumValue=(min(data)%/%classwidth)*classwidth # to calculate a value less than the minimum value in the data set.
MaximumValue=((max(data)%/%classwidth)+1)*classwidth
d=MaximumValue+classwidth #to get the last upper class limit
lowerclass=seq(minimumValue,MaximumValue,classwidth) # to get a sequence of all lower class limit.
upperclass=lowerclass+classwidth-1 #to form a sequence of all upperclass limit.
classInterval=paste(lowerclass,'-',upperclass) # the sequence of the labels for each class.
alldata=table(cut(data,seq(minimumValue-1,d-1,classwidth), labels=classInterval)) # to tabulate the data
mytable=data.frame(alldata) # turn the table to two column 
mytable
}
 #the functions code end here 
score=c(24, 46, 16, 33, 16, 13, 28, 19, 47, 49, 8, 56, 20, 26, 28, 29, 30, 18, 19, 15, 47, 32, 14, 25, 14, 16, 23, 12, 14, 13) 
#now call the function
createGroupTable(score,15)

Result>>

   Var1    Freq
1  0 - 9     1
2 10 - 19   13
3 20 - 29    8
4 30 - 39    3
5 40 - 49    4
6 50 - 59    1
7 60 - 69    0

'
If you tried this with different data set and provide your preference class-width you will realize that there is additional class at the last that we never need at all that is a flawless from the codes. So, I need to adjust that by removing the last row.

How to remove the last rows of a table using R.

to remove the last row here is never a problem, all i need to do is to find the index of the last row, then use form a new data without it. like the following:

Codes>>

createGroupTable=function(data,classwidth){ 
minimumValue=(min(data)%/%classwidth)*classwidth # to calculate a value less than the minimum value in the data set.
MaximumValue=((max(data)%/%classwidth)+1)*classwidth
d=MaximumValue+classwidth #to get the last upper class limit
lowerclass=seq(minimumValue,MaximumValue,classwidth) # to get a sequence of all lower class limit.
upperclass=lowerclass+classwidth-1 #to form a sequence of all upperclass limit.
classInterval=paste(lowerclass,'-',upperclass) # the sequence of the labels for each class.
alldata=table(cut(data,seq(minimumValue-1,d-1,classwidth), labels=classInterval)) # to tabulate the data
mytable=data.frame(alldata) # turn the table to two column 
lastIndex=length(mytable$Freq)
newTable=mytable[-lastIndex,]
newTable}

 #the functions code end here 
score=c(24, 46, 16, 33, 16, 13, 28, 19, 47, 49, 8, 56, 20, 26, 28, 29, 30, 18, 19, 15, 47, 32, 14, 25, 14, 16, 23, 12, 14, 13) 
#now call the function
createGroupTable(score,10)

Result>>

  Var1     Freq
1  0 - 9     1
2 10 - 19   13
3 20 - 29    8
4 30 - 39    3
5 40 - 49    4
6 50 - 59    1

Can you see that we have eliminate the last index. You can call the functions as many times as you want for any large data set, just input the variable name of the data and your class width.
Now I need to deal with other steps. These are not going to take time.

how to create group frequency table with class boundaries using R.

Since we are able to construct class interval with frequency now we need to subtract 0.5 from all lower class and add 0.5 to all upper classes. Study the following codes.

createGroupTable=function(data,classwidth){ 
minimumValue=(min(data)%/%classwidth)*classwidth
MaximumValue=((max(data)%/%classwidth)+1)*classwidth
d=MaximumValue+classwidth
lowerclass=seq(minimumValue,MaximumValue,classwidth)
 upperclass=lowerclass+classwidth-1
classInterval=paste(lowerclass,'-',upperclass)
lowerclassBound=lowerclass-0.5
upperclassBound=upperclass+0.5
classBoundary=paste(lowerclassBound,'-', upperclassBound)
alldata=table(cut(data,seq(minimumValue-1,d-1,classwidth), labels=classInterval))
mytable=data.frame(alldata)
mytable$classBound=classBoundary
pureTable=mytable[!(mytable$Freq==0),]
pureTable
}
 #the functions code end here 
score=c(24, 46, 16, 33, 16, 13, 28, 19, 47, 49, 8, 56, 20, 26, 28, 29, 30, 18, 19, 15, 47, 32, 14, 25, 14, 16, 23, 12, 14, 13) 
#now call the function
createGroupTable(score,10)

Result

  Var1     Freq  classBound
1   0 - 9    1  -0.5 - 9.5
2 10 - 19   13  9.5 - 19.5
3 20 - 29    8 19.5 - 29.5
4 30 - 39    3 29.5 - 39.5
5 40 - 49    4 39.5 - 49.5
6 50 - 59    1 49.5 - 59.5

Now we should include the codes to calculate the classMark(x) and Fx.
See the codes below.

createGroupTable=function(data,classwidth){ 
minimumValue=(min(data)%/%classwidth)*classwidth
MaximumValue=((max(data)%/%classwidth)+1)*classwidth
d=MaximumValue+classwidth
lowerclass=seq(minimumValue,MaximumValue,classwidth)
 upperclass=lowerclass+classwidth-1
classInterval=paste(lowerclass,'-',upperclass)
lowerclassBound=lowerclass-0.5
upperclassBound=upperclass+0.5
classBoundary=paste(lowerclassBound,'-', upperclassBound)
classMark=(lowerclass+upperclass)/2
alldata=table(cut(data,seq(minimumValue-1,d-1,classwidth), labels=classInterval))
mytable=data.frame(alldata)
Freq=mytable$Freq
Fx=Freq*classMark
mytable$classBound=classBoundary
mytable$classMark(x)=classMark
mytable$Fx=Fx
pureTable=mytable[!(mytable$Freq==0),]

pureTable
}
 #the functions code end here 
score=c(24, 46, 16, 33, 16, 13, 28, 19, 47, 49, 8, 56, 20, 26, 28, 29, 30, 18, 19, 15, 47, 32, 14, 25, 14, 16, 23, 12, 14, 13) 
#now call the function
createGroupTable(score,10)

Result>>

     Var1 Freq  classBound classMark    Fx
1   0 - 9    1  -0.5 - 9.5       4.5   4.5
2 10 - 19   13  9.5 - 19.5      14.5 188.5
3 20 - 29    8 19.5 - 29.5      24.5 196.0
4 30 - 39    3 29.5 - 39.5      34.5 103.5
5 40 - 49    4 39.5 - 49.5      44.5 178.0
6 50 - 59    1 49.5 - 59.5      54.5  54.5

As you can see above we just include two more columns. Now we can go ahead and calculate for the mean using £Fx/£F i.e the sum of Fx column divided by the sum of frequency column.
To do that we would add few lines of codes.
I shall show you that later in my next article including the standard deviation.
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Happy coding!🖐️🖐️

construct box plot of any data set using R.

maxwizard01 — Tue, 29 Mar 2022 07:55:51 +0000

How to construct boxplot of univariate data.

The boxplot is used to summarize data succinctly, quickly displaying if the data is symmetric or has
suspected outliers. It is based on the 5-number summary. In its simplest usage, the boxplot has a box with lines at
the lower quartile (basically Q1), the Median(Q2), the upper quartile (basically Q3) and whiskers which extend to the minimum and maximum value of the data set.

To make box and whisker plot, you have to make use of the boxplot() function. Before we take a look at different example on it let me explain some arguments the function takes.

data: this is your data set,it can be in the form of a data.frame (or list) from which the variables in formula should be taken.
main: this is use to write the Headings or Title of our graph.
xlab, ylab: these are x- and y-axis annotation, they are used to label the x and y-axis respectively. To use them just assign your labels to them.
col: it is used to give the box of the plot color. you can assign any color you like to beautify the graph.
border: this is used to give border coloran optional vector of colors for the outlines of the boxplots. The values in border are recycled if the length of border is less than the number of plots.
horizontal: logical indicating if the boxplots should be horizontal. it is FALSE by default which means vertical boxes. if assigned to be TRUE then we experienced horizontal boxes.
width
a vector giving the relative widths of the boxes making up the plot. it is usually used when you are comparing two or more plot.
outline: this take only TRUE or FALSE as its value. if outline is FALSE, then outliers are not drawn.
plot: this is the whole boxplot graph it is TRUE by default

If change to FALSE, the summaries which the boxplots are based on are returned while the graph will not be display.
notch: if notch is TRUE, a notch is drawn in each side of the boxes.

Now let's start taking a look at example to see how it works.

Example1

draw a box plot for the following data showing the score of 25 student in statistics.
24 46 16 33 16 13 28 19 47 49 8 56 20 26 28 29 30 18 19 15 47 32 14 25 14 .

Codes>>

scores=c(24, 46, 16, 33, 16, 13, 28, 19, 47, 49,  8, 56, 20, 26, 28, 29, 30, 18, 19, 15, 47, 32, 14, 25, 14)
boxplot(scores)

Result>>

As you can see we just plot simple boxplot. However to beautify our graph let us make use of the next three agument(main,xlab and ylab,color) listed above. copy and study the following codes.

scores=c(24, 46, 16, 33, 16, 13, 28, 19, 47, 49,  8, 56, 20, 26, 28, 29, 30, 18, 19, 15, 47, 32, 14, 25, 14)
boxplot(scores,main="THE SCORE OF STUDENTS IN STATISTICS",xlab='The box-plot', ylab='Scores',col="red")

Result>>

as you can see through the graph that exactly what was assigned to each of them reflect on the graph. let us apply more argument to the codes.

How to add border-color and draw horrzontal boxplot

here instead of vertical box we would have horizontal, also we would also have a value assigned to border. take a look at the following codes.
Codes>>

scores=c(24, 46, 16, 33, 16, 13, 28, 19, 47, 49,  8, 56, 20, 26, 28, 29, 30, 18, 19, 15, 47, 32, 14, 25, 14)
boxplot(scores,main="THE SCORE OF STUDENTS IN STATISTICS",xlab='Scores', ylab='The box-plot',col="black",border='green',horizontal=TRUE)

Result>>

Now I beleived you should be able to understand what is going on here. I have changed the color if you check the codes, Also the labels have been swapped because the box is now horrizontal.

let us see the useful of more parameters.I will be implementing width, outline and notch consider the following example.

Example

construct box plots to show the comparison between the following data showing the score of mathematics students and physics students in sta114.
Mathematics Student: 34, 44, 25,44, 29,46, 59, 40, 33, 45,27,34, 44, 28, 49.
Physics Students: 44, 56, 35, 49, 39, 22, 49, 20, 60, 39, 50, 55, 51, 30, 39.

maths=c(34, 44, 25, 44, 29,46, 59, 40, 33, 45, 27,34, 44, 28, 49)
physics=c(44, 56, 35, 49, 39, 22, 49, 20, 60, 39, 50, 55, 51, 30, 39)
boxplot(maths,physics,main="THE SCORE OF STUDENTS IN STATISTICS",ylab='Scores', xlab='The box-plot',col="black",border='green',horizontal=FALSE)

Result>>

all the argument used in the graph above are what you already know however let's make use of some others. observe the following codes

maths=c(34, 44, 25, 44, 29,46, 59, 40, 33, 45, 27,34, 44, 28, 49)
physics=c(44, 56, 35, 49, 39, 22, 49, 20, 60, 39, 50, 55, 51, 30, 39)
boxplot(maths,physics,main="THE SCORE OF STUDENTS IN STATISTICS",ylab='Scores', xlab='The box-plot',col="black",border='green',horizontal=FALSE,width=c(1,2),notch=TRUE)

Result>>

the notch you we used has cut off some part of the box and make a zigzag shape as you can see. the width here we assigned means one ratio two. and if you observed the graph you will realized that the second graph width is twice the first one. if you have 3 boxplot you should provide 3 value inside the vectors.

For outline and plot let us take a look at the following example.

Example

represent the following height of 15 male measure in Kg in box plot
4,8 24, 19, 18, 15, 22, 21, 24, 25, 23, 24, 23, 18, 17.

Codes>>

height<-c(4,8, 24, 19, 18, 15, 22, 21, 24, 25, 23, 24, 23, 18, 17)
boxplot(height,main="THE HEIGHT OF FIFTEEN MEN",ylab='Scores', xlab='The box-plot',col="green",border='black')

Result>>

the small circles you are looking below the box is what we called outlier. the indicate extremely small or large observation in the data set. to avoid this in our plot we will make use of the outline. like below

Codes>>

height<-c(4,8, 24, 19, 18, 15, 22, 21, 24, 25, 23, 24, 23, 18, 17)
> boxplot(height,main="THE HEIGHT OF FIFTEEN MEN",ylab='Scores', xlab='The box-plot',col="green",border='black',outline=FALSE)

Result>>

can you see how interesting it is?? now let disabled the plot using plot argument.
codes>>

height<-c(4,8, 24, 19, 18, 15, 22, 21, 24, 25, 23, 24, 23, 18, 17)
> boxplot(height,main="THE HEIGHT OF FIFTEEN MEN",ylab='Scores', xlab='The box-plot',col="green",border='black',outline=FALSE,plot=FALSE)

Result>>

$stats
     [,1]
[1,] 15.0
[2,] 17.5
[3,] 21.0
[4,] 23.5
[5,] 25.0

$n
[1] 15

$conf
         [,1]
[1,] 18.55227
[2,] 23.44773

$out
[1] 4 8

$group
[1] 1 1

$names
[1] ""

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Happy Coding :)

How to group large data set into classes using R.

maxwizard01 — Fri, 25 Mar 2022 12:26:36 +0000

How to create table for group Data

most of the time as a statisticians or analyst you will be dealing with big data
which might make you need grouping for a convenient view of your data. Imagine your data was given like below.

Example

the following shows the wages of employee in a month.

88,82,96,102,104,106,104,24,26,29,86,36, 60, 23, 24,39,48, 46, 33, 36,39, 78,67,82, 32, 67, 27, 24,26,27, 30,36, 37,49, 50, 56,83, 99,68, 28, 55, 54, 26,29, 30,40, 46, 44, 99,84, 36,51, 86,88, 87,29, 40, 40, 40, 66, 45,23,26, 46,46, 96,99, 100,100, 101,103, 106, 107, 46,48, 49,48, 94,55, 56,59, 60, 70, 72,76, 79,80, 50,49, 93,86, 54,83, 89,90, 94, 96, 99,102,46

what do I need to do when there large range and the element of the data hardly repeat itself??

what is class width??

A class width is just the number of element/value that could possibly be in a class.
for example if a class has the range 21-25 and 20-29 we would say their classwidth is 5 and 10 respectively. that happen because the element that could be consider to be in each class is below.
21-25 : 21,22,23,24 and 25 (5 numbers)
20-29 : 20, 21,22,23,24,25,26,27,28 and 29 (10numbers).

what is the trick to quickly get the classwidth of any class??
the trick I ususlly used is just by finding the range of the class and add 1.
i.e class-width=Range-1
so, for 21-25 ==>Range=25-21 = 4, class-width=4+1 =5.

Now if you look at the data above how do you think we should group them??well this is very easy even if your data is as large as hundreds, thousanads even millions.

How to group my large data set in to Class

To group your data set it is important to know the minimum and maximum value of you data, so as to know where the class should start and end and how large your class width should be.

How to calculate the min and maximum value.
to calculate the minimum and maximum value here make use of the min() and max()functions. for example let us find the maximum and minimum value of the data above. we will write the following codes to do that.

data=c(88,82,96,102,104,106,104,24,26,29,86,36,60,23,24,39,48,46,33,36,39,78,67,82,32,67,27,24,26,27,30,36,37,49,50,56,83,99,68,28,55,54,26,29,30,40,46,44,99,84,36,51,86,88,87,29,40,40,40,66,45,23,26,46,46,96,99,100,100,101,103,106,107,46,48,49,48,94,55,56,59,60,70,72,76,79,80,50,49,93,86,54,83,89,90,94,96,99,102,46)
min(data)
max(data)

Result>>

23
107

the codes above shows that the minimum value is 23 and the max value is 107.
Now to group this data we can start from 21 and end at 110 since between this range is all our data set will fall. another question will be "what should we use as our class width?", that one you can picture it yourself. you can decided to use 10 or 15. any of the two is okay but here i will be using 15.
Note: you can use any class width it depends on how big the range of your data set is. just make sure you group them into 5 to 15classes.

How do I Group my data set using R.
I believed you already understand the theoretical way to construct the data now let us see how to do it using code.
Before we write the codes, u should know the following

Important functions needed to construct group frequency table in R.

seq(): it is used to form a sequence of numbers, it takes three important argument;from,to and by. i.e the start,end and increment.
cut(): the function used to divide large data set into classes by stating the upper class limit of each class in a sequence. it takes 3important argument; data,break,label and include.lowest.
table(): to tabulate any data set given or represent it in a tabular form.

Now let's make use of the above functions to solve the problem.
Codes>>>

myData=c(88,82,96,102,104,106,104,24,26,29,86,36,60,23,24,39,48,46,
  33,36,39,78,67,82,32,67,27,24,26,27,30,36,37,49,50,56,83,
  99,68,28,55,54,26,29,30,40,46,44,99,84,36,51,86,88,87,29,
  40,40,40,66,45,23,26,46,46,96,99,100,100,101,103,106,107,
  46,48,49,48,94,55,56,59,60,70,72,76,79,80,50,49,93,86,54,
  83,89,90,94,96,99,102,46)
groupData=cut(myData,break=seq(20,110,15),include.lowerclass=FALSE)
table(groupData)

Result>>

 (20,35]  (35,50]  (50,65]  (65,80]  (80,95] (95,110] 
    19       27       10       10       16       18

the result above shows each class and their respective frequency using class width of 15.

How does the Codes work??

One particular thing I usually emphasis on is "understand how the codes work if you want codes to work for you". so I will explain more on how the parameters for cut() function works.

first parameter is the data-set, second is break; this is used to show how we want to break the class. since I already know the where my class will start and end together with the class width, then it will be nice to use seq() function to show the breaking point for each class.

the third parameters could be set to true or false, but I use False here because I know I am not going to include 20 in the first class, remember my target is between 21 and 110.


myData=c(88,82,96,102,104,106,104,24,26,29,86,36,60,23,24,39,48,46,
  33,36,39,78,67,82,32,67,27,24,26,27,30,36,37,49,50,56,83,
  99,68,28,55,54,26,29,30,40,46,44,99,84,36,51,86,88,87,29,
  40,40,40,66,45,23,26,46,46,96,99,100,100,101,103,106,107,
  46,48,49,48,94,55,56,59,60,70,72,76,79,80,50,49,93,86,54,
  83,89,90,94,96,99,102,46)
lowerclass=seq(21,110,15)
upperclass=lowerclass+14
classInterval=paste(lowerclass,'-',upperclass)
groupData=cut(myData,breaks=seq(20,110,15),
labels=classInterval,include.lowerclass=FALSE)
table(groupData)

Result>>

21 - 35 36 - 50 51 - 65 66 - 80 81 - 95 96 - 110
   19      27      10      10      16      18

How the codes work
if you try to run seq(21,110,15) you will realized that this gives you exactly the lower class limit for each class. you should be careful here as what we wanna deal with here is exactly how to write it in our natural ways instead of using bracket.
so, to get the upper class we know we need to add the class width but remember you must subtract 1.
Now we can definately match both together to form the range. paste() is the function used here to deal with that task. then I add labels to the cut() parameters letting it equal to the classInterval I just created. and boom! we did it.

This is quite interesting! but if you are someone like me I will like it if the table is two column table and how do I do that?? very easy, just make use of data.frame() function and you are done. take a look at the following codes.

Codes>>

  myData=c(88,82,96,102,104,106,104,24,26,29,86,36,60,23,24,39,48,46,
  33,36,39,78,67,82,32,67,27,24,26,27,30,36,37,49,50,56,83,
  99,68,28,55,54,26,29,30,40,46,44,99,84,36,51,86,88,87,29,
  40,40,40,66,45,23,26,46,46,96,99,100,100,101,103,106,107,
  46,48,49,48,94,55,56,59,60,70,72,76,79,80,50,49,93,86,54,
  83,89,90,94,96,99,102,46)
lowerclass=seq(21,110,15)
upperclass=lowerclass+14
classInterval=paste(lowerclass,'-',upperclass)
wages=cut(myData,breaks=seq(20,110,15),
                    labels=classInterval,include.lowerclass=FALSE)
groupTable=table(wages)
data.frame(groupTable)

Result>>

    wages    Freq
1   21 - 35   19
2   36 - 50   27
3   51 - 65   10
4   66 - 80   10
5   81 - 95   16
6  96 - 110   18

This is incredible right?? I hope you enjoy this article?? if yes then don't forget to share it to some else who might interested. you can drop me a comment if you have any question or correction. don't forge to follow me on Instagram, or Facebook you can also DM on whatsApp should have anything to discuss with me feel free for anything. Thanks!

How to calculate critical value using R.

maxwizard01 — Fri, 25 Mar 2022 12:22:05 +0000

how to calculate the critical value using R

one of the important aspect of analsis is doing test. confidence interval, hpothesis etc all need critical value either Ztest or ttest, one tail or two tails. whichever we can easil calculate them using R. let go into it.

How to calculate critical value using Normal Distribution

to calculate the critical value using Z-test all that is need is just one function provided that ou know all the important parameters.

Normal distribution function
qnorm(): this is the function use to get the critical value, it can accept the following parameter.
a) sd: this is the standard deviation it equal to 1 b default standard deviations.
b) mean: this is the vector mean it is 0 b default
c) p: the probabilit given(level of significant is written here in decimal)
d) lower.tail: this is the tails ou are dealing with it is true b default, it can be assigned to False to walk in right tail. Hence when true and input level of significant our answer will surel be negative. otherwise it will be positive.

Let's take a look at the following examples

Example1

What is the critical value of a normal distribution data given 98% as confidence level assuming you are doing left tail test??

Solution

Step1:
CL=98%
α=1−CL=1−0.98=0.02
Here alpha=0.02 (no need to divide b 2 since it is one tailed test)
Then we can proceed and assigned P to the function! like below

z=qnorm(p=0.02)
print(z)

Result>>

-2.053749

the above result is negative because it is lower tail, to do right tail then the code will look like the following
Codes>>

z=qnorm(p=0.02, lower.tail=FALSE)
print(z)

Result>>

2.053749

Note: TRUE o FALSE in capital letter.

Example2

What is the critical value when alpha is 5% assuming it is two tailed test.

Solution

Step1
Here α=5
α/2=0.05/2=0.025 (since it is two tailed test)

Step2 Now that we already know the important value we can easily know the z using codes below

Codes>>

z=qnorm(p=0.025, lower.tail=FALSE)
print(z)

Result>>

1.959964

you can even use codes to calculate the alpha ourselves before using the qnorm() function like below

alpha=0.05
half_alpha=0.05/2 #this will divide alpha b 2
z==qnorm(p=half_alpha, lower.tail=FALSE)
print(z)

Result>>

1.959964

As you can see we did everything b declaring variable names. we will still get the same result. I hope you understand that?

How to calculate critical value from t-table

To get the critical value from t-table you will use qt() function. this functions takes the following parameters.

a) p: the probability given(level of significant is written here in decimal)
b) df: this is the degree of freedom it is calculated b subtracting 1 from the sample size.
d) lower.tail: this is the tails ou are dealing with it is true b default, it can be assigned to False to walk in right tail. Hence when true and input level of significant our answer will surely be negative. otherwise it will be positive.

Example1

what will be the critical value of sample of size 18 with confidence level of 95%??

Solution

CL=95% =0.95 α=1−CL=1−0.95=0.05
α/2==0.05/2(working in two tails)
α/2=0.5/100=0.025(toDecimal)
n=9,df=n−1
df=18−1=17

Now let's write the codes
Codes>>

t=qt(p=0.025,df=17)
print(t)

you can also decide not to write each parameters and just input the value like the following but make sure df follows the alpha level immediately.

Codes

t=qt(0.025,17)
print(t)

Example 3

what will be the critical value of sample of size 28 with alpha level of 1% assuming it is one tail test??

Solution

α=0.01(toDecimal)
n=9,df=n−1
df=28−1=27

Now let's input the codes
Codes

t=qt(0.001,27)
print(t)

To avoid negative value if ou are working with right tail let lower.tail equal FALSE like the following

Codes

t=qt(0.025,17,lower.tail=FALSE)
print(t)

Result>>

2.109816

you can compute the whole calculation to free yourself from working by declaring some variable name like below

alpha=0.01
n=28
df=n-1
t=qt(alpha,df,lower.tail=FALSE)
print(t)

this will do all the calculation for you and print out the result.

I hope you find this article helpful?? like and comment below. you can also message me on whatsApp. feel free to ask any question it is our guy Max-wizard!

correlation and Regression using R programming

maxwizard01 — Sat, 26 Jun 2021 00:32:25 +0000

How do I calculate correlation using R programming??

To calculate correlation between two data sets is quite easy all you need is to make use of cor() function and insert the parameters xand y.

Example1

What is the correlation between X and Y if y = (100,94,150,160,180), and x = (23,21,32,40,45).

Solution

Codes>>

y=c(100,94,150,160,180)
x =c(23,21,32,40,45)
cor(x,y)

Result>>

> y=c(100,94,150,160,180)
> x =c(23,21,32,40,45)
> cor(x,y)
[1] 0.978522

Example2

What is the correlation between X and Y if y =(100,94,150,160,180,80), and x = (23,21,32,40,45, 10).

Solution

Codes>>

y=c(100,94,150,160,180,80)
x =c(23,21,32,40,45, 10)
cor(x,y)

Result>>

> y=c(100,94,150,160,180,80)
> x =c(23,21,32,40,45, 10)
> cor(x,y)
[1] 0.972529

How to calculate the regression

To deal with regression there are two values very important they are : the beta and the alpha. they are used to form the equation that connect the two items.
i.e y=bx + a. where a and b represent the alpha and beta respectively.
note: alpha is the intercept why b is the slope.

How do I calculate the beta and alpha of regression using R programming.

To calculate your alpha and beta using code we make use of lm() function.
where the parameters are place inside the lm() functions. let's take a look at some examples

Example1

If x = [23,21,32,40,45, 10] and y = [100,94,150,160,180,80]. Obtain the linear model of the relationship between y and x.
Solution

Codes>>

y=c(100,94,150,160,180,80)
x =c(23,21,32,40,45, 10)
lm(y ~ x)

Result>>

> y=c(100,94,150,160,180,80)
> x =c(23,21,32,40,45, 10)
> lm(y ~ x)

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)            x  
     39.693        3.075

Conclusion: from the result above alpha =39.693 while Beta=3.075.
and the equation is Y=3.075x+39.693

Example2

If x = [23,21,32,40,45] and y = [100,94,150,160,180]. Obtain the linear model of the relationship between y and x.

Solution

Codes>>

y=c(100,94,150,160,180)
x =c(23,21,32,40,45)
lm(y ~ x)

Result>>

>  y=c(100,94,150,160,180)
>  x =c(23,21,32,40,45)
>  lm(y ~ x)

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)            x  
     22.071        3.563

Conclusion: from the result above alpha =22.071 while Betaa=3.563.
and the equation is Y=3.563x+22.071.

Example3

If x = [23,21,32,40,45, 10] and y = [100,94,150,160,180,80]. What would be the value of y if x = 20.

Solution.

Note the we already write codes for this item in Example1. and our equation is Y=3.075x+39.693. so let's find the value of y when x=20.

codes>>

x=20
Y=3.075*x+39.693 
print(Y)

Result>>

> x=20
> Y=3.075*x+39.693 
> print(Y)
[1] 101.193

Example4

If x = [23,21,32,40,45, 10] and y = [100,94,150,160,180,80]. What would be the value of x if y = 200

Solution.

Note the we already write codes for this item in Example1. and our equation is Y=3.075x+39.693. since we need to find x when y=200 therefore we have to make x the subject of the formula.
Working that out we get x=(Y-39.693)/3.075. Now let's write the codes.

Codes>>

Y=200
x=(Y-39.693)/3.075
print(x)

Result>>>

> Y=200
> x=(Y-39.693)/3.075
> print(x)
[1] 52.13236

Yeah. that is how easy it is to use codes to solve most of the problem relating with correletion and regressions. I hope you find this article helpful? Alright you can chat me up if you have any doubt or observation on 07045225718 or 09153036869 it is still your guy Maxwizard. Enjoy coding!

How to calculate confidence interval using R.

maxwizard01 — Fri, 25 Jun 2021 00:13:34 +0000

How to calculate confidence interval of a proportion using R.

confidence interval of a proportion is now one of the important aspect of statistics use in everyday life in fact almost all big company make use of it especially those companies with artificial intelligent and tech.
let's take a look at some questions and see how R could have be of help to solve it.

Question1

What is the critical value if n = 100 and confidence interval is 99%?
1.96
2.32
2.63
1.68
2.58

Question2

Out 1500 students in Idia hostel, 1000 are allergic to Zikites so often avoid Zik hall route. Half of the remaining proportion wouldn't use Indy route as well. Obtain 95% confidence interval of the true population proportion of students who would use Zik route?
[0.6353, 0.6981]
[0.3019, 0.3647]
[0.8145, 0.8522]
[0.3095, 0.3572]
[0.8085, 0.8582]

Question3

In the last revision class, 0.7 actively participated. What is the standard error if the population of students in attendance was 2500?
0.038
0.21
0.029
0.458
No answer

Question4

If we use a ______ confidence percentage, then our margin of error will be _______.
[small, large]
[small, small]
[large, small]
[medium, large]
[large, large]

Question5

Out 1500 students in Idia hostel, 1000 are allergic to Zikites so often avoid Zik hall route. Half of the remaining proportion wouldn't use Indy route as well. Obtain 95% confidence interval of the true population proportion of students who wouldn't use Indy route?
[0.1478, 0.186]
[0.1418, 0.1915]
[0.1505, 0.1828]
[0.8145, 0.8522]
[0.8085, 0.8582]

Question6

A study finds that out of 2305 Awoites, 1383 Awoites are friends with Katangites. What is the margin of error, at 95% confidence interval?
4%
2%
4.5%
2.5%
3%

Question7

What is the critical value if n = 20 and confidence interval is 99%?
2.54
2.63
2.86
1.96
2.58

Question8

Given that the MOE is ±4.5%. At 95% confidence interval and standard deviation of 2, what is the sample size?
0.7588
76
7588
7588.34
75.88

Question9

Out 1500 students in Idia hostel, 1000 are allergic to Zikites so often avoid Zik hall route. Half of the remaining proportion wouldn't use Indy route as well. Obtain 95% confidence interval of the true population proportion of students who wouldn't use Zik route?
[0.6353, 0.6981]
[0.3019, 0.3647]
[0.6428, 0.6905]
[0.8145, 0.8522]
[0.8085, 0.8582]

Question10

A study finds that 0.6 of every Awoite are friends with Zikites. If the MOE is 2%. How many Awoites are friends with Zikites?
2304.96
2305
23
23.05

SOLUTION
firstly I will create a robot that will keep solving the questions that look alike so the codes are:

# for confidence Interval when given a proportion,number of population and the confidence level
confidenceInterval=function(p,n,confidenceLevel){
pn=p/n
q=1-pn
alpha=1-confidenceLevel
me=abs(qnorm(alpha/2))*sqrt(pn*q/n)
CI=p+me
CI2=p-me
print(CI)
print(CI2)
}

# To calculate the confidence Interval proportions when  proportion,number of population and the confidence level are given 
confprops=function(proportionSize,populationSize,confidenceLevel){
  pproportion=proportionSize/populationSize
  qproportion=1-pproportion
  alpha=1-confidenceLevel
  marginerror=abs(qnorm(alpha/2))*sqrt(pproportion*qproportion/n)
  CI=pproportion+marginerror
  CI2=pproportion-marginerror
  print(CI)
  CI2
}

# To Calculate the margin error when given proportion size,poputlation size and confidence level
marginOfError=function(proportionSize,populationSize,confidenceLevel){                                                        
  p=proportionSize/populationSize
  q=1-p
  alpha=1-confidenceLevel
  zscore=abs(qnorm(alpha/2))
  marginOfError=zscore*sqrt(p*q/populationSize)
  marginOfError
}

To calculate the population size when margin error, confidence level and standard deviation is given.
size=function(marginOfError,confidenceLevel,standardDeviation){
  alpha=1-confidenceLevel
  zscore=abs(qnorm(alpha/2))
          size=(zscore*standardDeviation/marginOfError)^2
          size
}

Copy the code above and paste. then you have just created a robot for most of the questions we need to solve concerning the topic.

for question1

To calculate the critical value we calculate the zscore of the half-alpha.
where alpha=1-confidence level
Codes>>

confidenceLevel=99/100
alpha=1-confidenceLevel
half_alpha=alpha/2
criticalValue=abs(qnorm(half_alpha))
print(criticalValue)

Result>>

> confidenceLevel=99/100
> alpha=1-confidenceLevel
> half_alpha=alpha/2
> criticalValue=abs(qnorm(half_alpha))
> print(criticalValue)
[1] 2.575829

Question2,5,9

Note that the number of student that will use the Zik's route are 500. s0, P-value=500, n=1500,ConfidLevel=95%=0.95. so we use our robot and call the function.
Also those that will not use indy in question5 are 250. because half of 500 is 250.
so, P-value=250, n=1500,ConfidLevel=95%=0.95.
Question9 is also similar those that will not use zik are 1000.
so, P-value=1000, n=1500,ConfidLevel=95%=0.95
codes>>

# To calculate the confidence Interval proportions when  proportion,number of population and the confidence level are given 
confprops=function(proportionSize,populationSize,confidenceLevel){
  pproportion=proportionSize/populationSize
  qproportion=1-pproportion
  alpha=1-confidenceLevel
marginerror=abs(qnorm(alpha/2))*sqrt(pproportion*qproportion/populationSize)
  CI=pproportion+marginerror
  CI2=pproportion-marginerror
  print(CI)
  CI2
}
confprops(500,1500,0.95)
 confprops(250,1500,0.95)
 confprops(1000,1500,0.95)

Result>>

> > confprops=function(proportionSize,populationSize,confidenceLevel){
+   pproportion=proportionSize/populationSize
+   qproportion=1-pproportion
+   alpha=1-confidenceLevel
+   marginerror=abs(qnorm(alpha/2))*sqrt(pproportion*qproportion/populationSize)
+   CI=pproportion+marginerror
+   CI2=pproportion-marginerror
+   print(CI)
+   CI2
+ }
> confprops(500,1500,0.95)
[1] 0.3571893
[1] 0.3094774
> confprops(250,1500,0.95)
[1] 0.1855264
[1] 0.1478069
> confprops(1000,1500,0.95)
[1] 0.6905226
[1] 0.6428107

Question3.

for question 3 we are given the proportion already and the population size.
so standardError= stanadardDeviation/sqrt(N) or square root of {p(1-p)/n}. now our P=0.7 and n=2500. so we solve with codes
Codes>>>

p=0.7
q=1-p
n=2500
standardError=sqrt(p*q/n)
print(standardError)

Result>>|

p=0.7
>       q=1-p
>       n=2500
>       standardError=sqrt(p*q/n)
>       print(standardError)
[1] 0.009165151

Question4

This is very direct as we all known that the higher the confidence level the bigger the margin of error needed.
Question6
here we need margin of error just copy the code I have written for it as robot. and call the function substituting respective value.
N=2305 P=1383 CL=0.95

size,poputlation size and confidence level
marginOfError=function(proportionSize,populationSize,confidenceLevel){                                                        
  p=proportionSize/populationSize
  q=1-p
  alpha=1-confidenceLevel
  zscore=abs(qnorm(alpha/2))
  marginOfError=zscore*sqrt(p*q/populationSize)
  marginOfError
}
marginOfError(1383,2305,0.95)

Result>>

> marginOfError=function(proportionSize,populationSize,confidenceLevel){                                                        
+   p=proportionSize/populationSize
+   q=1-p
+   alpha=1-confidenceLevel
+   zscore=abs(qnorm(alpha/2))
+   marginOfError=zscore*sqrt(p*q/populationSize)
+   marginOfError
+ }
> marginOfError(1383,2305,0.95)
[1] 0.01999946

Notice: if you approximate this you get 0.02. which is the same as 2%.

Question8.

Firstly we make N the subject of the formula. that give us
size(N)=(zscore*standardDeviation/marginOfError)^2.
that is how we make the robot using the important parameters. now let's see the codes when ME=0.45,CL=0.95,SD=2

size=function(marginOfError,confidenceLevel,standardDeviation){
  alpha=1-confidenceLevel
  zscore=abs(qnorm(alpha/2))
          size=(zscore*standardDeviation/marginOfError)^2
          size
}
size(0.045,0.95,2)

Results>>

> size=function(marginOfError,confidenceLevel,standardDeviation){
+     alpha=1-confidenceLevel
+     zscore=abs(qnorm(alpha/2))
+     size=(zscore*standardDeviation/marginOfError)^2
+     size
+ }
> size(0.045,0.95,2)
[1] 7588.067

Question10.

from question6 it is clear that there are 2305 of awoite. so
P=0.6,N=2305, ME=0.02.
since Confidence interval = P+ or - ME
so, confidence interval =0.6+0.02 =0.62
number of student friendly with zik =0.62*2305= 1429
since we are given the proportion we multiply by the total population to get the actual value.
so actually No answer but we pick something likely to be answer.
I hope you find this article helpful??

if you have any question don't hesitate to ask. chat me up on WhatsApp or Mail. Don't forget to follow me on Twitter so that you don't miss any of my articles.

How to plot Histogram using R-programming.

maxwizard01 — Wed, 02 Jun 2021 17:59:07 +0000

How to draw a Histograms

When visualizing a single numerical variable, a histogram will be our go-to tool, which can be created in R using the hist() function.

Let's quickly take a look at some examples.

Example1

construct a histogram for the following score of some students in thier first C.A.T

Codes

studentscore=c( 8,5,6,1,11,8,10, 15,4,3, 10,1,4,12,3, 14, 10,6,3,9,1,5,
     20,4,9,6,1,1,1,8,4,23,3,12,3,5, 16, 10,2,8,3, 22, 16,2
     ,1,1,5,4,2,3)
hist(studentscore)

Results

you can see histogram already done. but this is not perfect as it will be nice to add some design to it. To do that we make use of some parameters. inside the his() function.
some of the parameters are:

main : this is used to add title to your graph
col : this is used to add colour to your grapah(all the bar.)
xlab: to label the x-axis
ylab: to label the y-axis
col.main: this is to give the font-color to our Title.
probability: to find the probabilty and use it to plot the graph i.e the y-axis will range from 0 to 1. it is usually false by default.

Now let's take a look at some examples

Example2.

the following show the weigth of male living in an estate. represent them on histogram.
69,132,83,18,44,57,12, 131,34,26,84, 147,84,10,17,75,
83, 142, 158,25, 3, 2,55,34, 119,23, 202,157, 141,75,53,
157, 174,39,43,109, 115, 107, 120,64,87, 118,20,41, 130, 52, 67, 13, 17,81

Solution.

weight=c( 69,132,83,18,44,57,12, 131,34,26,84, 147,84,10,17,75,
 83, 142, 158,25, 3, 2,55,34, 119,23, 202,157, 141,75,53, 
 157, 174,39,43,109, 115, 107, 120,64,87, 118,20,41, 130, 52, 67, 13, 17,81)
hist(weight,main='The weight of males in Estate', col='pink',xlab='Weight(Kg)',ylab='Frequency')

Result

run the codes, did you get the same result?? Yeah, we just make use of col,main,xlab and ylab parameters. How about others?? well let's make use of them and see the result.

Example3

we are going to use the last example above to construct a beautiful one.

Codes

weight=c( 69,132,83,18,44,57,12, 131,34,26,84, 147,84,10,17,75,
 83, 142, 158,25, 3, 2,55,34, 119,23, 202,157, 141,75,53, 
 157, 174,39,43,109, 115, 107, 120,64,87, 118,20,41, 130, 52, 67, 13, 17,81)
hist(weight,main='The weight of males in Estate', col='pink',xlab='Weight(Kg)',ylab='Frequency',probability=TRUE,col.main='red')

Result.

can you see the result?? did you notice some changes?? what are they?? yes, the color of the title change from black to red. eh eh?? what other change can you see?? No!No! there is one more. umh? Now you get it. the yaxis has been change to some number less than 1. that is the work of probability when we assign it to "TRUE".

How do I give each of the bar of histogram different color using R??

well, if you are someone who love to use different color like me, then you can assign different color for each of the rectangle on the graph(the bar). let's see the example below.

Example

Here I will be using the mark of some student in statistics below:

32, 38, 13, 31, 60,56, 5,2, 14,9,33, 31,3, 24, 10, 33, 6,10,57, 22, 51,4, 12,11, 47, 10, 30, 31, 19, 44,8, 16,9, 49,8,2,5,4, 15,8,7, 37,2, 54, 47,1, 45,4,46, 20, 69
Codes>>


marks=c(32, 38, 13, 31, 60,56, 5,2, 14,9,33, 31,3, 24, 10, 33, 6,10,57, 22, 51,4, 12,11, 47, 10, 30, 31, 19, 44,8, 16,9, 49,8,2,5,4, 15,8,7, 37,2, 54, 47,1, 45,4,46, 20, 69)
Color=c('red','orange','blue','yellow','violet','pink')
hist(marks,main='The marks of students in Statistics',col=Color,xlab='Marks',ylab='Frequency',probability=TRUE,col.main='red')

Results>>

This result above look differents, notice I listed all my colors inside a vector named 'Colour' so the name was assigned to col parameters inside the histogram.

I hope you find this article helpful. consider to follow, or like on this platform. you can also chat me up if you have any addition or question on WhatsApp. follow me on instagram and don't forget to follow me on Twitter

How to plot a box plot using R

maxwizard01 — Sun, 30 May 2021 12:27:31 +0000

How do you construct a boxpot with ease using R

How to plot Boxplot in R-programming

box plot also is very similar to all others graphs in method. All we need to draw it is our data then the box plot() function.
let's see how it works.

Example

Represent the following weight of some students in boxpot.
1,3, 6, 1,3,3, 4, 3, 3, 1, 3 ,5 ,1, 2, 1 ,4, 3, 2 ,3 ,1 ,
1, 1 ,1, 4, 3, 1,5,5

Codes

weight=c(1,3, 6, 1,3,3, 4, 3, 3, 1, 3 ,5 ,1, 2, 1 ,4, 3, 2 ,3 ,1 ,1, 1 ,1, 4, 3, 1,5,5)
boxplot(weight)

Result>>

Now that is nice, how about given it color and title?? then we can make use of some other parameters in boxplot() function. they are :
main: to write the main title of the graph
col: to give preferable colour for our boxpot.
col.main : to give a preferable font color of our main title
xlab: to give a label on x axis
ylab: to give a label on y axis
border: to give a preferable color for the border instead of black.
let's practice it and see how it works

Example2

use the weights in example to plot boxplot.
codes>>

weight=c(1,3, 6, 1,3,3, 4, 3, 3, 1, 3 ,5 ,1, 2,
         1 ,4, 3, 2 ,3 ,1 ,1, 1 ,1, 4, 3, 1,5,5)
boxplot(weight,
        ylab = "numbers",
        main = "The weight of some students.",
        col = "darkorange",
        col.main='red',border='green')

Result>>

One more thing is that you can have more than one boxplot on your graph, just list them in the boxplot() function.

Example
the following show the score of some student in mathematics and english. use the two data below to plot boxpot.
Mathematics={61,53, 46, 61,63,53, 44, 43, 43, 61, 33 ,45 ,31, 52, 51 ,54, 53, 44 ,38 ,51 ,41, 51 ,61, 44, 53, 61,45,55}
English = {51,43, 66, 51,43,33, 44, 53, 63, 41, 53, 45 ,51, 52,
61 ,44, 33, 42 ,53 ,61 ,61, 51 ,41, 44, 43, 41,45,45}
Solution.
Codes>>

Mathematics=c(61,53, 46, 61,63,53, 44, 43, 43, 61, 33 ,45 ,31, 52,    51 ,54, 53, 44 ,38 ,51 ,41, 51 ,61, 44, 53, 61,45,55)
English = c(51,43, 66, 51,43,33, 44, 53, 63, 41, 53, 45 ,51, 52,
         61 ,44, 33, 42 ,53 ,61 ,61, 51 ,41, 44, 43, 41,45,45)
boxplot(Mathematics,English
        ylab = "numbers",
        main = "The Mathematics and English Score of some students.",
        col = "orange",
        col.main='red',border='blue')

Result>>

Now I believe you now understand both stem and boxplot. I hope you find this article helpful?? consider to follow me. it's the guy Maxwizard. chat me up on whatsapp(07045225718) if you have any question on this or any big deal. enjoy coding!

How to plot stem and leaf in R-programming

maxwizard01 — Sun, 30 May 2021 12:21:15 +0000

Stem-and-leaf Charts

There are a range of graphical summaries of data. If the data set is relatively small, the stem-and-leaf diagram is
very useful for seeing the shape of the distribution and the values. It takes a little getting used to. The number on
the left of the bar is the stem, the number on the right the digit. You put them together to find the observation.
Suppose you have the box score of a basketball game and find the following points per game for players on both teams
21 13 16 23 14 12 14 13 22 10 10 20 16 28 21 14 14 18 22 15.
To create a stem and leaf chart is simple, all you need is the stem() function.
Let's try to solve the question above.
Codes>>

score=c(21, 13, 16, 23, 14, 12, 14, 13 ,22 1,20, 10, 20 ,16, 28 21,14,14,18,22,15)
stem(scores)

Result>>

> score=c(21, 13, 16, 23, 14, 12, 14, 13 ,22,13,20, 10, 20 ,16, 28, 21,14,14,18,22,15)
> stem(score)

  The decimal point is 1 digit(s) to the right of the |

  1 | 023334444
  1 | 5668
  2 | 0011223
  2 | 8

Can you see how easy it is?? let's try one more Example

Example2

Represent the following data in stem and leaf.
1,3, 6, 1,3,3, 4, 3, 3, 1, 3 ,5 ,1, 2, 1 ,4, 3, 2 ,3 ,1 ,1, 1 ,1, 4, 3, 1,5,5

Solution.
this is our codes below
Codes>>

data=c(1,3, 6, 1,3,3, 4, 3, 3, 1, 3 ,5 ,1, 2, 1 ,4, 3, 2 ,3 ,1 ,1, 1 ,1, 4, 3, 1,5,5)
stem(data)

Result>>

data=c(1,3, 6, 1,3,3, 4, 3, 3, 1, 3 ,5 ,1, 2, 1 ,4, 3, 2 ,3 ,1 ,1, 1 ,1, 4, 3, 1,5,5)
> stem(data)

  The decimal point is at the |

  1 | 0000000000
  2 | 00
  3 | 000000000
  4 | 000
  5 | 000
  6 | 0

Exercise
use the following marks to plot a stem and leaf.
46,47,60,40,54,29, 59, 50, 29, 59, 46, 51, 51, 50, 61,
32, 45, 42, 62, 62, 42, 37,28, 51, 41, 38,40, 41, 45, 59, 38,41,
45,34, 40, 59, 41,60, 54, 44, 56,53, 25 ,49,54, 58, 34, 60, 51, 25.

I hope this article satisfy your needs?? if so, then don't stop here try to read the next articles..

How to plot bar chart with R

maxwizard01 — Sat, 29 May 2021 10:52:53 +0000

How to plot bar graph in R.

One of the important aspect in statistics or data analysis is representing data in a graphical method. Today we are going to learn how to plot a common statistical graph called bar chart.

how can we plot bar chart with ease??

well, you don't have any problem concerning that. all you just need to use is the barplot() function.
let's see how its work.
Example 1
represent the following height of some student in primary one below in bar chart.
1,3, 6, 1,3,3, 4, 3, 3, 1, 3 ,5 ,1, 2, 1 ,4, 3, 2 ,3 ,1 ,1, 1 ,1, 4, 3, 1,5,5.
solution
To use the barplot function we declare a variable that will hold all the height given then we can insert it inside the function.

Codes>>

height= c(1,3, 6, 1,3,3, 4, 3, 3, 1, 3 ,5 ,1, 2, 1 ,4, 3, 2 ,3 ,1 ,1, 1 ,1, 4, 3, 1,5,5)
barplot(height) # this isn’t correct

Result>>

Now, looking at the result above, you can see the behaviour of the barplot() function. it draw a rectangle for each of the data which is not what we actually want. so how do we correct this?? well, the solution is to sumamarize the data into mark and frequency i.e counting the duplicate. then we can plot the summarized data.
how do we summarize the data??
To summarize the data, use the table() function. this table() function helps to count the occurrence of each data.
Now let's try to plot the graph again.

Codes>>

height= c(1,3, 6, 1,3,3, 4, 3, 3, 1, 3 ,5 ,1, 2, 1 ,4, 3, 2 ,3 ,1 ,1, 1 ,1, 4, 3, 1,5,5)
summarizedHeight=table(height)
barplot(summarizedHeight) # this correct

Result>>

Woow! we get exactly what we need!

However, what if we wish to design the graph by giving it title and color. won't that be more amazing??
well, that is just little thing.
How to label, title and color the graph with R.
the barplot() function accept more parameters apart from data which helps to do some certains task. the parameters are :

Vectors: is the data will want to use to plot the graph which is important to be summarised by table() function.
col: this is use to color your bar(the rectangular shape).
main: this is the main title of your graph.
xlab: to label on X-axis
ylab: to label on Y-axis.
col.main: this will give main title the preferable colour.

Now let's quickly take alook at how to implement this in our codes.
Example
use the data in example1 to plot a bar graph.
solution.
so, in this example we are going to make use of all the parameters above so that our chart look amazing.

Codes>>

height= c(1,3, 6, 1,3,3, 4, 3, 3, 1, 3 ,5 ,1, 2, 1 ,4, 3, 2 ,3 ,1 ,1, 1 ,1, 4, 3, 1,5,5)
summarizedHeight=table(height)
barplot(summarizedHeight,col = 'pink',main = 'The height of student in primary1',ylab="frequency",xlab = "Height",col.main='red')

Result>>

woow! it looks beautiful right?? good!. However, we still have some inbuilt functions and parameters that could be use to make our graph more perfect they are:
title() function
font.main
font.axis
sub
cex.main

cex.sub
font.sub
col.sub e.tc

that is a simple way to represent our data in bar chart. I hope you find this article helpful. consider to like, join me on histagram or chat me up on whatsapp(07045225718)