indiadigital
Home / Abhyas / Class 11 Maths / Mean deviation, variance and standard deviation
CLASS 11 MATHS · STATISTICS

Mean deviation, variance and standard deviation

Mean deviation about the mean = Σ|xᵢ − x̄|/n. Variance σ² = Σ(xᵢ − x̄)²/n = Σx²/n − x̄². Standard deviation σ = √variance.

Loading practice…

Worked examples

Example 1 · level 1

The maximum temperatures (°C) in Pune over 5 days are: 20, 21, 22, 25, 27. Find the mean deviation about the mean. (Give a fraction if needed.)

Show solution
  1. Mean = 23.
  2. Deviations: −3, −2, −1, 2, 4.
  3. Σ|xᵢ − x̄| = 12.
  4. MD = 12/5.

Answer: 12/5

Example 2 · level 2

The marks of 6 students in a unit test are: 44, 45, 48, 53, 54, 56. Find the variance. (Give a fraction if needed.)

Show solution
  1. Mean = 50.
  2. Deviations: −6, −5, −2, 3, 4, 6.
  3. Σ(xᵢ − x̄)² = 126.
  4. Variance = 126/6 = 21.

Answer: 21

Example 3 · level 3

For 20 observations, Σx = 160 and Σx² = 2,000. Find the standard deviation.

Show solution
  1. σ² = 100 − 8² = 100 − 64 = 36.
  2. σ = √36 = 6.

Answer: 6

Search by task, format or tool name.