If Arithmetic mean and coefficient of variation of x are 10 and 40 respectively, then the variance of y = 10 - 2x is:
64
Step 1 — Standard deviation of x from CV:
\[CV = \frac{\sigma_x}{\bar{x}} \times 100 \implies 40 = \frac{\sigma_x}{10} \times 100 \implies \sigma_x = 4\]
Step 2 — Variance of x:
\[\operatorname{Var}(x) = \sigma_x^{2} = 16\]
Step 3 — Apply \(\operatorname{Var}(a+bx)=b^{2}\operatorname{Var}(x)\):
For \(y = 10 - 2x\), \(b=-2\):
\[\operatorname{Var}(y) = (-2)^{2}\times 16 = 64\]
Therefore Var(y) = 64.
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?
