Mean, Median, and Mode
When working with data, one of the most common questions we ask is: What is the typical value?
Measures of central tendency help us answer this question. The three most important measures are: Mean, Median, and Mode.
What Is Mean?
The mean is commonly known as the average. It is calculated by adding all values and dividing by the total number of values.
Numerical Example
Consider the following exam scores:
60, 70, 80, 90, 100
Step 1: Add all values
60 + 70 + 80 + 90 + 100 = 400
Step 2: Divide by the number of values (5)
Mean = 400 ÷ 5 = 80
So, the average exam score is 80.
Real-World Example (Mean)
A company calculates the average monthly salary of employees to understand overall compensation levels.
However, very high or very low salaries can affect the mean.
What Is Median?
The median is the middle value when the data is arranged in ascending or descending order.
The median is useful when data contains extreme values (outliers).
Numerical Example (Odd Count)
Data (sorted):
10, 20, 30, 40, 50
The middle value is 30. So, the median is 30.
Numerical Example (Even Count)
Data (sorted):
10, 20, 30, 40
There are two middle values: 20 and 30.
Median = (20 + 30) ÷ 2 = 25
Real-World Example (Median)
When reporting house prices, the median is often preferred because a few extremely expensive houses do not distort the result.
What Is Mode?
The mode is the value that appears most frequently in a dataset.
A dataset may have:
- One mode (unimodal)
- More than one mode (bimodal or multimodal)
- No mode
Numerical Example
Data:
2, 4, 4, 6, 8
The value 4 appears most often. So, the mode is 4.
Real-World Example (Mode)
A clothing store may use mode to identify the most commonly sold shirt size.
Comparison: Mean vs Median vs Mode
| Measure | What It Represents | Best Used When |
|---|---|---|
| Mean | Average value | Data has no extreme outliers |
| Median | Middle value | Data contains outliers |
| Mode | Most frequent value | Identifying common categories |
Quick Check (Think Before Answering)
Data:
5, 10, 10, 15, 100
The value 100 is very large compared to others. Which measure best represents the center?
Practice Quiz
Question 1:
Which measure is most affected by extreme values?
Question 2:
Which measure can be used for categorical data?
Question 3:
If a dataset has two values occurring most frequently, what is it called?
Mini Practice (Real-World Thinking)
A company wants to report employee income fairly.
- Would mean or median be better?
- Why?
What’s Next
In the next lesson, we will study Range, Variance, and Standard Deviation, which explain how spread out the data is.