📈 Measure of Dispersion

Last Updated: Jan 2026

Measure of Dispersion tells us how spread out the data is around the central value.

🗣 Hinglish Tip: 👉 “Data values ek-dusre se aur mean/median se kitni door hain?” Dispersion = data ka failaav (spread)

It Help to :

Two datasets can have the same mean but very different spread.

Dispersion helps to:

• Measure data variability
• Judge consistency
• Compare datasets properly
• Quality control

Types of Measure of Dispersion

Main measures:

1. Range
2. Variance
3. Standard Deviation

Range

Range is the difference between the maximum and minimum values.

Formula

$Range = Max - Min$

Example

Data: 2, 4, 6, 10
Range = 10 - 2 = 8

Limitation

• Uses only two values
• Highly affected by outliers

🗣 Hinglish Tip: Range sirf boundary values dekhta hai

Variance

• Variance measures the average squared distance from the mean.
• If variance is small, the data is close to the mean.
• If variance is large, the data is far from the mean.
• If variance is zero, all data values are the same.
• It can be calculated for the population or sample.

Formula

1. Population Variance

$\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}$

Where:

• $(\sigma^2)$ = population variance
• $(x_i)$ = data values
• $(\mu)$ = population mean
• $(N)$ = population size

2. Sample Variance

$s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}$

Where:

Where:

• $(s^2)$ = sample variance
• $(\bar{x})$ = sample mean
• $(n)$ = sample size

🗣 Hinglish Tip: Sample variance me (n - 1) aata hai — correction ke liye

Example

Data: 2, 4, 6
Mean = 4

Squared deviations:

$(2 - 4)^2 = 4
(4 - 4)^2 = 0
(6 - 4)^2 = 4$

Variance:

$(4 + 0 + 4) / 3 = 2.67$

Standard Deviation

Standard Deviation is the square root of variance.

• It shows spread in same units as data.
• Easier to interpret
• Widely used in ML & analytics

Formula

Population Standard Deviation

$\sigma = \sqrt{\sigma^2}$

Sample Standard Deviation

$s = \sqrt{s^2}$

🗣 Hinglish Tip: SD = variance ka root, samajhna easy hota hai

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