Statistics (Mean Deviation, Variance, Standard Deviation) — Practice

Question 1

Find the mean deviation about the mean for: 2, 4, 5, 7, 8.

Accepted Answer

Mean x̄ = (2+4+5+7+8)/5 = 26/5 = 5.2. Deviations: |2−5.2|=3.2, |4−5.2|=1.2, |5−5.2|=0.2, |7−5.2|=1.8, |8−5.2|=2.8. Sum = 9.2. MD = 9.2/5 = 1.84.

Question 2

Find the variance and standard deviation of: 6, 8, 10, 12, 14.

Accepted Answer

Mean x̄ = (6+8+10+12+14)/5 = 50/5 = 10. Deviations from mean: −4, −2, 0, 2, 4. Squared deviations: 16, 4, 0, 4, 16. Sum = 40. Variance σ² = 40/5 = 8. Standard deviation σ = √8 = 2√2 ≈ 2.83.

Question 3

Two series A and B have: Series A — mean=40, SD=10; Series B — mean=20, SD=6. Which series is more consistent?

Accepted Answer

C.V.(A) = (σ_A/x̄_A)×100 = (10/40)×100 = 25%. C.V.(B) = (σ_B/x̄_B)×100 = (6/20)×100 = 30%. Since C.V.(A) = 25% < C.V.(B) = 30%, Series A is MORE CONSISTENT (less relative variation) than Series B.

Practice — Statistics (Mean Deviation, Variance, Standard Deviation)

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