JEE MAIN - Mathematics (2003 - No. 10)
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 :
$$\sum {{x^2}} = 2830$$, $$\sum x = 170$$
One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is :
188.66
177.33
8.33
78.00
Explanation
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
$$ = {{\sum {{x^2}} } \over N} - {\left( {{{\sum x } \over N}} \right)^2}$$
$$ = {{3330} \over {15}} - {\left( {{{180} \over {15}}} \right)^2}$$
$$ = 222 - {12^2}$$
$$ = 222 - 144$$
$$ = 78$$
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
$$ = {{\sum {{x^2}} } \over N} - {\left( {{{\sum x } \over N}} \right)^2}$$
$$ = {{3330} \over {15}} - {\left( {{{180} \over {15}}} \right)^2}$$
$$ = 222 - {12^2}$$
$$ = 222 - 144$$
$$ = 78$$
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