Measure of Central Tendency

Last Updated: Jan 2026

Measure of Central Tendency is used to find a single value that represents the center or typical value of a dataset.

🗣 Hinglish Tip: Central tendency = poore data ka ek representative number

Data Can Be In Form of:

• Population : All Data
• Sample : A Part of Data

Used in:

• Statistics
• Data Analysis
• Machine Learning
• Decision making

There are three main measures:

1. Mean
2. Median
3. Mode

Mean (Arithmetic Mean)

Mean is the average of all observations.

Formula

Population Mean

$\mu = \frac{x_1 + x_2 + x_3 + \cdots + x_n}{N}$

Where:

• $\mu$= population mean
• $x_i$ = each data value
• $N$= total number of observations

Sample Mean

$\bar{x} = \frac{x_1 + x_2 + x_3 + \cdots + x_n}{n}$

Where:

• $\bar{x}$ = sample mean
• $n$ = sample size

🗣 Hinglish Tip: Population ka mean = $\mu$ Sample ka mean = $\bar{x}$

Mean Example

Data:

$2, 4, 6, 8$

Mean:

$(2 + 4 + 6 + 8) / 4 = 5$

Median

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

Formula

Let n be number of observations.

• If n is odd:

Median = value at position (n + 1) / 2

• If n is even:

Median = average of values at positions n/2 and (n/2 + 1)

Median Examples

Odd number of values

Data: 3, 1, 5
Sorted: 1, 3, 5
Median = 3

Even number of values

Data: 2, 4, 6, 8
Median = (4 + 6) / 2 = 5

🗣 Hinglish Tip: Median = beech wali value, outliers ka effect kam

Mode

Mode is the value that appears most frequently in the dataset.

Formula

Mode = value with maximum frequency

Mode Example

Data: 1, 2, 2, 3, 4
Mode = 2

Notes:

• One mode → Unimodal
• Two modes → Bimodal
• More than two → Multimodal
• No repetition → No mode

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