JEE MAIN - Mathematics (2017 - 9th April Morning Slot - No. 9)
The sum of 100 observations and the sum of their squares are 400 and 2475,
respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If
the incorrect observations are omitted, then the variance of the remaining observations
is :
8.25
8.50
8.00
9.00
Explanation
We have
$$\sum\limits_{i = 1}^{100} {{x_i} = 400} $$
$$\sum\limits_{i = 1}^{100} {x_i^2 = 2425} $$
The variance of the remaining observations is
$${\sigma ^2} = {{\sum {x_i^2} } \over N} - {\left( {{{\sum {{x_i}} } \over N}} \right)^2}$$
$$ \Rightarrow {{2425} \over {97}} - {\left( {{{388} \over {97}}} \right)^2}$$
$$ \Rightarrow {{2425} \over {97}} - 16$$
$$ \Rightarrow {{2425 - 1552} \over {97}} = {{873} \over {97}} = 9$$
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