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

A

$6.5$

B

$2.87$

C

$3.87$

D

$8.25$

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The correct Answer is:D

Given number are 1,2,3,4,5,6,7,8,9, 10 and 11
$∴ Σ x_{i} = 2 + 3 + 4 + \dots \dots + 11$
$= \frac{10}{2} [2 \times 2 + 9 \times 1] = 5 [4 + 9] = 65$
$Σ x_{i}^{2} = 2^{2} + 3^{2} + 4^{2} + 5^{2} + \dots . + 11^{2}$
$= (1^{2} + 2^{2} + 3^{3} + \dots . + 11^{2}) - (1^{2}$
$= \frac{11 \times 12 \times 23 - 6}{6}$ =505
$∴ s^{2} = \frac{Σ_{i}^{2}}{n} - {(\frac{Σ x_{i}}{n})}^{2} = \frac{505}{10} - {(\frac{65}{10})}^{2}$
$= 505 - {(\frac{65}{10})}^{2}$
$505 - {(6.5)}^{2}$
$50.5 - 42.25$
=8.25

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Updated on:21/07/2023

Class 11 MATHS STATISTICS

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