For four different frequency distributions, the mean (M), mode (MD), and…
2025
For four different frequency distributions, the mean (M), mode (MD), and coefficient of variation (CV) are given below. Compute Pearson’s coefficient of skewness for each distribution and arrange the values in descending order.
Distribution | Mean (M) | Mode (MD) | CV |
|---|---|---|---|
A | 40 | 39 | 5% |
B | 50 | 54.375 | 35% |
C | 200 | 195.2 | 8% |
D | 150 | 147 | \(\frac{100}{3}\%\) |
Choose the correct answer from the options given below.
Answer: C. A, C, D, B — ConceptPearson's coefficient of skewness measures asymmetry relative to the standard deviation: Sk = (M − Mode)/σ. The coefficient of variation is CV = (σ/M)…
- A.
C, A, B, D
- B.
B, C, D, A
- C.
A, C, D, B
- D.
D, B, A, C
Show answer & explanation
Correct answer: C
Concept
Pearson's coefficient of skewness measures asymmetry relative to the standard deviation: Sk = (M − Mode)/σ.
The coefficient of variation is CV = (σ/M) × 100, so σ = (CV/100) × M. Compute σ first, then compare the signed skewness values.
Application
For A, σ = (5/100) × 40 = 2, so Sk = (40 − 39)/2 = 0.50.
For B, σ = (35/100) × 50 = 17.5, so Sk = (50 − 54.375)/17.5 = −0.25.
For C, σ = (8/100) × 200 = 16, so Sk = (200 − 195.2)/16 = 0.30.
For D, CV = 100/3%, hence σ = (1/3) × 150 = 50, so Sk = (150 − 147)/50 = 0.06.
Cross-check
A, C and D have positive skewness because their means exceed their modes, while B has negative skewness because its mean is below its mode. This independently confirms the signs and the relative placement of B.
Therefore, the descending order of the coefficients of skewness is A, C, D, B.