Measures of Central Tendency — Deep & Clear Explanation
Measures of central tendency are statistical tools used to describe the center or typical value of a dataset. They help us understand where most values lie and summarize large data into a single representative number.
The three main measures are:
Mean (Average)
Median
Mode
1️⃣ Mean (Arithmetic Mean)
🔹 Definition
The mean is the sum of all values divided by the total number of observations.
🔹 Formula
Mean =∑𝑥/𝑛
Where:
∑x = sum of all values
n = number of observations
🔹 Example
Marks: 10, 20, 30, 40, 50
Mean
10
+
20
+
30
+
40
+
50
5
150
5
30
Mean=
5
10+20+30+40+50
=
5
150
=30
🔹 When to Use Mean
Data is numerical
Data is symmetrical
No extreme values (outliers)
🔹 Advantages
✔ Uses all observations
✔ Useful for further mathematical analysis
✔ Easy to understand
🔹 Limitations
❌ Highly affected by outliers
Example with outlier:
Income: 10k, 12k, 15k, 18k, 1,00,000k
→ Mean becomes misleading
2️⃣ Median
🔹 Definition
The median is the middle value when data is arranged in ascending or descending order.
🔹 Steps to Find Median
Arrange data in order
If odd number of values → middle value
If even number → average of two middle values
🔹 Example (Odd count)
Data: 5, 10, 15, 20, 25
Median = 15
🔹 Example (Even count)
Data: 10, 20, 30, 40
Median =
20
+
30
2
25
2
20+30
=25
🔹 When to Use Median
Data contains outliers
Data is skewed
Income, salary, property prices
🔹 Advantages
✔ Not affected by extreme values
✔ Represents real-world data better in skewed cases
🔹 Limitations
❌ Does not use all data values
❌ Not suitable for advanced mathematical calculations
3️⃣ Mode
🔹 Definition
The mode is the value that occurs most frequently in the dataset.
🔹 Example
Data: 2, 4, 4, 6, 8
Mode = 4
🔹 Types of Mode
Unimodal – one mode
Bimodal – two modes
Multimodal – more than two modes
No mode – all values occur once
🔹 When to Use Mode
Categorical data
Identifying most popular item
🔹 Advantages
✔ Works with non-numeric data
✔ Easy to identify
🔹 Limitations
❌ May not represent entire dataset
❌ Sometimes no clear mode
📌 Comparison Table
Measure Uses All Data Affected by Outliers Best For
Mean ✅ Yes ❌ Yes Symmetrical data
Median ❌ No ✅ No Skewed data
Mode ❌ No ✅ No Categorical data
📉 Relationship Between Mean, Median & Mode
1️⃣ Symmetrical Distribution
Mean = Median = Mode
2️⃣ Positively Skewed (Right Skewed)
Mean > Median > Mode
3️⃣ Negatively Skewed (Left Skewed)
Mean < Median < Mode
🎯 Real-World Examples
Scenario Best Measure Reason
Student marks Mean No extreme values
Salaries Median High income outliers
Shoe size in shop Mode Most demanded size
Customer rating Median/Mode Skewed ratings
🔍 Importance in Data Science & Business
Since you work with data science and analytics, these measures help in:
Understanding data distribution
Feature analysis
Data pre-processing
Business decisions
Dashboard insights (Tableau / Power BI)
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