Question

If x_i | f_i, i = 1, 2 … n is a frequency distribution with standard deviation 15 and mean 30, the coefficient of variation will be equals to:
1. 2
2. 200
3. 0.5
4. 50

Answer 1

Correct Answer - Option 4 : 50

Given

X_i/f_i I = 1, 2, ----n is a frtequency distribution

Standard deviation = σ = 15

Mean = x̅ = 30

Formula

Coefficient of variation = CV = σ/x̅ ) × 100

Calculation

⇒ CV = (15/30) × 100

∴ The coefficient of variance is 50%

Imp

Standard deviation = σ = ∑(x – x̅)²]/n

x = observations

x̅ = mean

n = number of observation

Coefficient of variation = The coefficient of variation shows the extent of variability of data in a sample in relation to the mean of the population.

The coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investmernt.