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Coefficient of Variation

In an experim...

Question

$I n a n e x p e r i m e n t w i t h 15 o b s e r v a t i o n s, t h e r e s u l t s a r e a s f o l l o w s : \sum x^{2} = 2830, \sum x = 170. O n e o b s e r v a t i o n t h a t w a s 20 w a s f o u n d t o b e w r o n g a n d w a s r e p l a c e d b y t h e c o r r e c t v a l u e 30. T h e n t h e c o r r e c t e d v a r i a n c e i s$

A

78.00

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B

188.66

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C

177.33

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D

8.33

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Solution

The correct option is A 78.00
$n = 15; \sum x^{2} = 2830; \sum x = 170 (\sum x^{2}) C o r r e c t e d = 2830 - (20)^{2} + (30)^{2} = 3330 (\sum x) C o r r e c t e d = 170 - 20 + 30 = 180 σ^{2} = \frac{3330}{15} = (\frac{180}{15})^{2} ∴ σ^{2} = \frac{\sum x^{2}}{n} = {(\frac{\sum x}{n})}^{2} = 222 - 144 = 78$

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