Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Consider the first 10 positive integers. If we multiply each number by –1 and then add 1 to each number, the variance of the numbers so obtained is A. 8.25 B. 6.5 C. 3.87 D. 2.87

Consider the first 10 positive integers. If we multiply each number by –1 and then add 1 to each number, the variance of the numbers so obtained is
A. 8.25
B. 6.5
C. 3.87
D. 2.87

Answers (1)

First 10 positive integers are 1,2, 3, 4, 5,6 ,7, 8,9, 10  On multiplying each number by 

-1 we get-1, -2, -3, -4 , -5, -6, -7, -8, -9 , -10 

  On adding 1 to each of the number, we get 0, -1, -2, -3, -4, -5, -6, -7, -8, -9  

\\ \Sigma x_{i}=0-1-2-3-4-5-6-7-8-9=-45~ and \\ \\ ~ \Sigma x_{i}^{2}=0^{2}+ \left( -1 \right) ^{2}+ \left( -2 \right) ^{2}+ \ldots \ldots + \left( -9 \right) ^{2}~ \\ \\ \text{ But we know that } \Sigma x_{i}^{2}=\frac{9 \left( 9+1 \right) \left( 2 \left( 9 \right) +1 \right) }{6}=285 \\ \\ \sigma = \sqrt {\frac{ \Sigma x_{i}^{2}}{n}- \left( \frac{ \Sigma x_{i}}{n} \right) ^{2}}~ \\ \\ \text{Substituting the corresponding values, we get }\sigma =\sqrt {28.5- \left( -4.5 \right) ^{2}}=\sqrt {28.5-20.25}= \sqrt {8.25}~ \\ \\ \text{Now for variance both the sides are squared } \sigma ^{2}=8.25 \\

 

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question