First slide

Introduction to statistics

Question

Consider the numbers 1,2,3,4,5,6,7,8,9 and 10. If 1 is added to each number, the variance of the numbers so obtained is

Easy

A

6.5
B

2.87
C

3.87
D

8.25

Solution

Given numbers are 1,2,3, 4, 5, 6, 7, 8, 9 and 10.
If 1 is added to each number, then observations will be 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11
$\begin{matrix} ∴ {Σx}_{i} = 2 + 3 + 4 + \dots + 11 \\ = \frac{10}{2} [2 \times 2 + 9 \times 1] = 5 [4 + 9] = 65 \end{matrix}$
$\begin{matrix} and {Σx}_{i}^{2} = 2^{2} + 3^{2} + 4^{2} + 5^{2} + \dots + 11^{2} \\ = (1^{2} + 2^{2} + 3^{2} + \dots + 11^{2}) - (1^{2}) \\ = \frac{11 \times 12 \times 23}{6} - 1 = 505 \\ ∴ s^{2} = \frac{{Σx}_{i}^{2}}{n} - {(\frac{{Σx}_{i}}{n})}^{2} = \frac{505}{10} - {(\frac{65}{10})}^{2} \\ = 50 .5 - (6 .5)^{2} \\ = 50 .5 - 42 .25 \\ = 8 .25 \end{matrix}$

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