In an experiment with 15 observations the following results were available : Σx2=2830,Σx=170One observation that was 20 was found wrong and was replaced by the correct value 30. The corrected variance is

In an experiment with $15$ observations the following results were available :
$Σ x^{2} = 2830, Σ x = 170$
One observation that was $20$ was found wrong and was replaced by the correct value $30 .$ The corrected variance is

A
$8.33$
B
$78.00$
C
$188.66$
D
$177.33$

Solution:

We have,

Corrected $Σ x^{2} = 2830 - 20^{2} + 30^{2} = 3330$

Corrected $Σ x = 170 - 20 + 30 = 180$

$∴$ Corrected Variance $= \frac{3330}{15} - {(\frac{180}{15})}^{2} = 78$

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