First slide

Introduction to statistics

Question

The sum of the squares deviations for $10$ observations taken from their mean $50$ is $250 .$ The coefficient of variation is

Moderate

A

$10 %$
B

$40 %$
C

$50 %$
D

none of these

Solution

Let $x_{1}, x_{2}, \dots, x_{10}$ be $10$ observations. Then,
$\sum_{i = 1}^{10} {(x_{i} - 50)}^{2} = 250$
$∴ σ^{2} = \frac{1}{10} \sum_{i = 1}^{10} {(x_{i} - 50)}^{2} = \frac{250}{10} = 25 \Rightarrow σ = 5$
$∴$ Coefficient of variation $= \frac{σ}{\bar{X}} \times 100 = \frac{5}{50} \times 100 = 10 %$

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