The sum of 100 observations and the sum of their squares are 400 and 2475, respectively.

Question

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:

Accepted Answer

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

$${\sigma ^2} = {{\sum {x_i^2} } \over N} - {\left( {{{\sum {{x_i}} } \over N}} \right)^2}$$

$$ \Rightarrow {{2425} \over {97}} - {\left( {{{388} \over {97}}} \right)^2}$$

$$ \Rightarrow {{2425} \over {97}} - 16$$

$$ \Rightarrow {{2425 - 1552} \over {97}} = {{873} \over {97}} = 9$$

Solutions · 1