Approximately, the coefficient of variation for the given data where Pearson's second measure of skewness = 0.42, arithmetic mean = 86 and median = 80, is:
50
Step 1 — Find the standard deviation using Pearson's second skewness:
\[Sk_p = \dfrac{3(\bar{x} - M)}{\sigma} \Rightarrow 0.42 = \dfrac{3(86 - 80)}{\sigma} = \dfrac{18}{\sigma}\]
\[\sigma = \dfrac{18}{0.42} \approx 42.857\]
Step 2 — Compute the coefficient of variation:
\[CV = \dfrac{\sigma}{\bar{x}} \times 100 = \dfrac{42.857}{86}\times 100 \approx 49.83\%\]
Rounded to the nearest option, CV ≈ 50.
Important Questions from Coefficient of Variation
Consider the following statements:
1. Coefficient of variation depends on the unit of measurement of the variable.
2. Range is measure of dispersion.
3. Mean deviation is least when measured about median.
Which of the above statements are correct?In a study of two groups, the following results were obtained:
Group A
Group B
Sample size
20
25
Sample mean
22
23
Sample standard deviation
10
12
Which of the following statements is correct?
