What does “central tendency” mean?

Measures of central tendency are methods to find a single number that represents the “center” of a dataset.

1) Mean (Arithmetic Mean)

Meaning (simple)

Mean is the “usual average.” It is found by adding all values and dividing by how many values are there.

Formula

If values are 𝓍1​,𝓍2​,𝓍3​,…,𝓍n

$\bar{x}=\frac{\sum x}{n}$

Example (Marks)

Data: 2, 3, 3, 4, 8

$\bar{x}=\frac{2+3+3+4+8}{5}=\frac{20}{5}=4$

$\bar{x}=\frac{2+3+3+4+8}{5}=\frac{20}{5}=4$

=52+3+3+4+8​=520​=4

2) Median

Meaning (simple)

Median is the middle value when the data is arranged in ascending order.

Steps

First sort the data.

• If n is odd, Median = middle value
• If n is even, Median = average of the two middle values

Formula / Position

• If n is odd: Median is at position $\frac{n+1}{2}$
• If n is even: Median is average of values at positions $\frac{n}{2}$​ and ( $\frac{n}{2}+1$)

Example (odd n)

Data (sorted): 2, 3, 3, 4, 8

so middle position $=\frac{5+1}{2}=3$

3rd value is 3, so Median = 3

3) Mode

Meaning

Mode is the value that occurs most frequently.

“Formula”

There’s no fixed formula just count frequencies and find the highest.

Example

Data: 2, 3, 3, 4, 8 3 occurs two times (highest), so Mode = 3

One diagram that students understand quickly

Data (sorted)

2, 3, 3, 4, 8

Number line diagram (text diagram you can copy into your paper)

2   3   3   4   8
|---|---|---|---|
        ↑
     Median = 3

Mode = 3 (comes most)

Mean = 4 (because total 20 ÷ 5 = 4)

Quick comparison (very important in exams)

Mean uses all values (can change a lot if one value is very big or very small).

Median is the middle (best when there are outliers).

Mode is the most common (useful for “most repeated” value).

Swathika B

Swathika B is an MBA graduate in Finance & Business Analytics , the founder of The Commerce Lab. With a strong academic foundation in B.Com BFSI and hands-on experience in financial analysis, data analytics, and business studies, she created this platform to make Commerce and Accountancy simple, practical, and exam-ready for students across India.