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13.Statistics
hard
In an experiment with $15$ observations on $x$, the following results were available $\sum {x^2} = 2830$, $\sum x = 170$. On observation that was $20$ was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is..
A
$78$
B
$188.66$
C
$177.33$
D
$8.33$
(AIEEE-2003)
Solution
(a) $\sum x = 170$, $\sum {x^2} = 2830$
Increase in $\sum x = 10$, then $\sum x' = 170 + 10 = 180$
Increase in $\sum {x^2} = 900 – 400 = 500$, then
$\sum {x'^2} = 2830 + 500 = 3330$
Variance $ = \frac{1}{n}\sum {x'^2} – {\left( {\frac{{\sum x'}}{n}} \right)^2}$
$ = \frac{{3330}}{{15}} – {\left( {\frac{{180}}{{15}}} \right)^2} = 222 – 144 = 78$.
Standard 11
Mathematics
