In an experiment with 15 observations on x, then following results were available: [ x^2 =…

Question

In an experiment with 15 observations on $x$, then following results were available:

$$\sum {{x^2}}  = 2830$$, $$\sum x  = 170$$

One observation that was 20 was found to be wrong and was replaced by the correct value
30. Then the corrected variance is :

Accepted Answer

Given that,

N = 15,  $$\sum {x{}^2}  = 2830,\,\sum x  = 170$$

As, 20 was replaced by 30 then,

$$\sum x  = 170 - 20 + 30 = 180$$

and $$\sum {{x^2}}  = 2830 - 400 + 900 = 3330$$

So, the corrected variance

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

$$ = {{3330} \over {15}} - {\left( {{{180} \over {15}}} \right)^2}$$

$= 222 - {12^2}$

$= 222 - 144$

$= 78$

Solutions · 1