Example 1 · level 1
Find the standard deviation (population, divide by n) of: 12, 7, 8, 11. Give two decimals.
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- Mean = 38 ÷ 4 = 9.5.
- Squared deviations: 6.25, 6.25, 2.25, 2.25; sum = 17.
- Variance = 4.25; σ = √4.25 = 2.06.
Answer: 2.06
CA FOUNDATION: QUANTITATIVE APTITUDE · MEASURES OF CENTRAL TENDENCY AND DISPERSION
Standard deviation of a small data set
σ = √[Σ(x − x̄)² ÷ n]. Find the mean, square each deviation, average them, then take the square root.
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Worked examples
Example 2 · level 2
Find the standard deviation (population, divide by n) of: 17, 4, 4, 13, 5. Give two decimals.
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- Mean = 43 ÷ 5 = 8.6.
- Squared deviations: 70.56, 21.16, 21.16, 19.36, 12.96; sum = 145.2.
- Variance = 29.04; σ = √29.04 = 5.39.
Answer: 5.39
Example 3 · level 3
Find the standard deviation (population, divide by n) of: 27, 27, 29, 32, 27, 31. Give two decimals.
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- Mean = 173 ÷ 6 = 28.8333.
- Squared deviations: 3.3611, 3.3611, 0.0278, 10.0278, 3.3611, 4.6944; sum = 24.8333.
- Variance = 4.1389; σ = √4.1389 = 2.03.
Answer: 2.03