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

$\begin{array}{1 1}(A)\; 6.5 \\(B)\;2.87 \\(C)\;3.87 \\(D)\;8.25 \end{array} $

1 Answer

The formula to calculate variance $\sigma^2 = \large\frac{\sum x^2}{n} - \bigg( \large\frac{\sum x}{n}\bigg)^2$
Adding a constant to each numbers, does not affect the value of the variance.
It remain the same.
As calculated SD in the previous problem for 1st 10 natural numbers
Variance $=(SD)^2$
$\qquad= (2.87)^2=8.25$
and adding 1 to each numbers will not change the value of the variance.
Hence D is the correct answer.
answered Jul 9, 2014 by meena.p

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