📈 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, the data is uniformly distributed.
  • It calculates By the population or sample.

Formula

1.Population Variance

σ² = Σ(xᵢ − μ)² / N

Where:

  • σ² = population variance
  • xᵢ = data values
  • μ = population mean
  • N = population size

2.Sample Variance

s² = Σ(xᵢ − x̄)² / (n − 1)

Where:

  • s² = sample variance
  • x̄ = 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 interpretation
  • Widely used in ML & analytics

Formula

Population Standard Deviation

σ = √σ²

Sample Standard Deviation

s = √s²

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

← PreviousNext →