First slide

Introduction to statistics

Question

$Let x_{1}, x_{2}, x_{3}, x_{4} and x_{5} be the observations with mean m and standard deviation s . The standard deviation of the$
$observations k x_{1}, k x_{2}, k x_{3}, k x_{4} and k x_{5} is$

Moderate

A

$s + k$
B

$\frac{s}{k}$
C

ks
D

s

Solution

$\begin{array}{l} Here, m = \frac{Σ x_{i}}{5}, s = \sqrt{\frac{Σ x_{i}^{2}}{5} - {(\frac{Σ x_{i}}{5})}^{2}} \\ For observations k x_{1}, k x_{2}, k x_{3}, k x_{4}, k x_{5}, \\ \begin{aligned} SD & = \sqrt{\frac{k^{2} Σ x_{i}^{2}}{5} - {(\frac{k Σ x_{i}}{5})}^{2}} \\ = \sqrt{\frac{k^{2} Σ x_{i}^{2}}{5} - k^{2} {(\frac{Σ x_{i}}{5})}^{2}} = k \sqrt{(\frac{Σ x_{i}^{2}}{5}) - {(\frac{Σ x_{i}}{5})}^{2}} = k s \end{aligned} \end{array}$

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