First slide

Introduction to statistics

Question

$If \sum_{i = 1}^{5} (x_{i} - 100) = 5 and \sum_{i = 1}^{5} {(x_{i} - 100)}^{2} = 25, then the standard deviation of observations$ $2 x_{1} + 73, 2 x_{2} + 73, 2 x_{3} + 73, 2 x_{4} + 73, 2 x_{5} + 73 is$

Moderate

A

8
B

16
C

4
D

2

Solution

$\begin{array}{l} Given that \sum_{i = 1}^{5} (x_{i} - 100) = 5 and \sum_{i = 1}^{5} {(x_{i} - 100)}^{2} = 25 \\ Standard deviation of observations 2 x_{1} + 73, 2 x_{2} + 73, 2 x_{3} + 73, 2 x_{4} + 73, 2 x_{5} + 73 is \end{array}$
$σ (2 x_{1} + 73) = 2 σ (x_{i})$
$= 2 \sqrt{\frac{\sum_{i = 1}^{n} {x_{i}}^{2}}{n} - {(\frac{\sum_{i = 1}^{n} x_{i}}{n})}^{2}}$
$= 2 \sqrt{\frac{\sum_{i = 1}^{5} {(x_{i} - 100)}^{2}}{5} - {(\frac{\sum_{i = 1}^{5} (x_{i} - 100)}{5})}^{2}}$
$= 2 \sqrt{\frac{25}{5} - {(\frac{5}{5})}^{2}}$
$= 2 \sqrt{5 - 1}$
$= 4$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App