If the mean of the frequency distribution is 28, then its variance is _______.

Question

If the mean of the frequency distribution is 28, then its variance is \_\_\_\_\_\_\_.

Answer: 151

Accepted Answer

Let the class marks with an unknown frequency variable $x$ give: $\bar x = \dfrac{10+45+25x+175+130}{14+x}=28$

$$28(14+x) = 410+25x \implies 392+28x = 410+25x \implies 3x=18 \implies x=6$$

$$\text{Variance} = \frac{1}{N}\sum f_ix_i^2-(\bar x)^2 = \frac{18700}{20}-(28)^2 = 935-784 = 151$$

Solutions · 1