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Statistics with R - Measures of Central Tendency and Measures of Dispersion

#r #tutorial #statistics #math

mtcars 

data(mtcars)
head(mtcars)
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Loads and displays the first few rows of the mtcars dataset.

str(mtcars)
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Displays the structure of the mtcars dataset, showing the type of each column.

summary(mtcars)
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Measures of Central Tendency

Mean

μ=1N∑i=1Nxi \mu = \frac{1}{N} \sum_{i=1}^{N} x_i

Calculates the mean of a sequence of numbers.

n = c(1,2,4,5,6)

print(n)

mean_ = sum(n) / length(n)

print(mean_)
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mean_cyl = sum(mtcars$cyl) / length(mtcars$cyl) 

print(mean_cyl)
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Median

  • If ( N ) is odd:
Med=x(N+12) \text{Med} = x_{\left(\frac{N+1}{2}\right)}
  • If ( N ) is even:
Med=x(N2)+x(N2+1)2 \text{Med} = \frac{x_{\left(\frac{N}{2}\right)} + x_{\left(\frac{N}{2} + 1\right)}}{2}

Calculates the median of a sequence of numbers with an odd size.

data_even <- c(7, 13, 19, 33, 67)

median_ <- median(data_even)
print(median_)

data_even <- c(7, 13, 19, 33, 67)
n = length(data_even)
median_ <- data_even[(n + 1) / 2]
print(median_)
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Calculates the median of a sequence of numbers with an even size.

data_odd <- c(2, 34, 76, 92, 112)

median_ <- median(data_odd)
print(median_)

data_odd <- c(2, 34, 76, 92, 112)
n = length(data_odd)

median_ <- (data_odd[n / 2] + data_odd[n / 2 + 1]) / 2

print(median_)
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median(mtcars$cyl)
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median(mtcars$qsec)
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Mode

Mode=argmax⁡xi f(xi) \text{Mode} = \underset{x_i}{\operatorname{argmax}} \ f(x_i)

Creates a frequency table for a sequence of numbers.

numbers <- c(1, 233, 233, 010101, 342, 1, 2, 1111, 1, 55)

tnumbers <- table(numbers)
print(numbers)
print(tnumbers)
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mode_ <- as.numeric(names(tnumbers)[tnumbers == max(tnumbers)])
print(mode_)
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Identifies the most frequent value(s) in the sequence of numbers.

library(DescTools)
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mode_ <- Mode(tnumbers)
print(mode_)
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Measures of Dispersion

Defines a sequence of numbers.

n_arr = c(1,2,4,5,6)
print(n_arr)
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Variance

σ2=1N∑i=1N(xi−μ)2 \sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2

Calculates the variance of a sequence of numbers.

mean_ <- mean(n_arr)

print('Mean')
print(mean_)

print('Variance')
var_ <- sum((n_arr - mean_)^2) / length(n_arr)

print((n_arr - mean_))
print((n_arr - mean_)^2)
print(sum((n_arr - mean_)^2))
print(length(n_arr))
print(var_)
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Standard Deviation

σ=σ2 \sigma = \sqrt{\sigma^2}

Calculates the standard deviation, which is the square root of the variance.

print('Variance')
var_ <- sum((n_arr - mean_)^2) / length(n_arr)
print((n_arr - mean_))
print((n_arr - mean_)^2)
print(sum((n_arr - mean_)^2))
print(length(n_arr))
print(var_)

print('Standard Deviation')
std_ <- sqrt(var_)
print(std_)
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Calculates the standard deviation using the sd function in R.

std_ <- sd(n_arr)
print(std_)
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Range

Range=xmax−xmin \text{Range} = x_{\text{max}} - x_{\text{min}}

Calculates the range, which is the difference between the maximum and minimum values.

range_ <- max(n_arr) - min(n_arr)
print('Range')
print(max(n_arr))
print(min(n_arr))
print(range_)
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Calculates the range using the diff function.

range_ <- diff(range(n_arr))
print(range_)
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Coefficient of Variation

CV=σμ \text{CV} = \frac{\sigma}{\mu}

Calculates the coefficient of variation, which is the ratio of the standard deviation to the mean.

mean_ <- mean(n_arr)
print('Mean')
print(mean_)

print('Variance')
var_ <- sum((n_arr - mean_)^2) / length(n_arr)
print((n_arr - mean_))
print((n_arr - mean_)^2)
print(sum((n_arr - mean_)^2))
print(length(n_arr))
print(var_)

print('Standard Deviation')
std_ <- sqrt(var_)
print(std_)

print('Coefficient of Variation')
cv <- std_ / mean_
print(cv)
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sc0v0ne

This blog is to create some posts about subjects that I am studying and I share them to help other users.

A little more about me...

Graduated in Bachelor of Information Systems, in college I had contact with different technologies. Along the way, I took the Artificial Intelligence course, where I had my first contact with machine learning and Python. From this it became my passion to learn about this area. Today I work with machine learning and deep learning developing communication software. Along the way, I created a blog where I create some posts about subjects that I am studying and share them to help other users.

I'm currently learning TensorFlow and Computer Vision

Curiosity: I love coffee

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