Difference Between Mean and Median Explained
In
statistics, two of the most commonly used measures of central tendency are mean
and median. Many students get confused between mean and median because
both represent the “average” of a dataset. However, they are calculated
differently and are used in different situations. Let us understand the difference
between mean and median explained in a simple and clear way.
What is
Mean?
The mean
is generally known as the average. It is calculated by adding all the values in
a dataset and dividing the total by the number of values.
Formula
for Mean:
Example:
Find the
mean of the following numbers.
4, 7, 3, 5,
1
Solution:
Step 1: Add
the numbers.
4 + 7 + 3 + 5 + 1 = 20
Step 2:
Divide the sum by total numbers (5).
20 ÷ 5 = 4
So, the mean
is 4.
The concept
of mean is widely used in mathematics and statistics and is strongly connected
with the ideas developed in probability theory.
What Is
Median?
The median
is the middle value in a dataset when the numbers are arranged in ascending
(smallest to largest) or descending (largest to smallest) order.
Steps to
Find Median:
1.
Arrange
numbers in order.
2.
Find
the middle number.
If there is:
- Odd number of values → The middle value is the
median.
- Even number of values → Take the average of the two
middle numbers.
Example 1
(Odd Number of Values):
Numbers: 2, 5,
8, 10, 13
The middle
number is 8.
So, median = 8
Example 2
(Even Number of Values):
Numbers: 3, 6,
7, 9, 12, 15
The middle
numbers are 7 and 9.
Average = (7
+ 9) ÷ 2 = 8
So, median =
8
Key
Differences Between Mean and Median
|
Mean |
Median |
|
Sum of
values ÷ total number |
Middle
value in ordered data |
|
Affected
by extreme values (outliers) |
Not
affected much by extreme values |
|
Used in
symmetric data |
Used in
skewed data |
Effect of
Outliers
An important
difference appears when extreme values are present.
Example:
2, 3, 4, 5, 100
Mean = (2 +
3 + 4 + 6 + 100) ÷ 5 = 115 ÷ 5 = 23
Median = 4
Here, the
mean is heavily influenced by 100, but the median is not affected. That is why
median is preferred when data has very high or very low values.
When to
Use Mean?
- Test match scores
- Scientific calculations
- Financial averages
- When data is evenly distributed
When to
Use Median?
- Income data
- Real estate prices
- Skewed distributions
- When outliers exist
Conclusion
The mean
gives the overall average by using all values in the dataset, while the median
gives the middle value after rearranging the data in order. The mean is
sensitive to extreme numbers, but the median is more stable in such cases.
Understanding the difference between mean and median helps in analysing data correctly and choosing the right measure depending on the situation.