In an experiment with 15 observations on x- the following results were available- - x2 -2830- - x -170 One observation that was 20 was found to be wrong and was replaced by the correct value 30- The corrected variance is-

∑ x =170, ∑ x^2 =2830 Increase in ∑ x =30 20=10, then ∑ x'=170+10=180 Increase in ∑ x^2 = 30^2 20^2=900 400=500 then ∑ x'^2=2830+500=3330 Variance =1/n∑ x'^2 ...

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Standard XII

Mathematics

Standard Deviation

In an experim...

Question

In an experiment with 15 observations on $x$ , the 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 $30$ . The corrected variance is:

8.33

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78.00

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188.66

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177.33

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Solution

The correct option is B
78.00

$\sum x = 170, \sum x^{2} = 2830$
Increase in $\sum x = 30 - 20 = 10$ , then
$\sum x^{'} = 170 + 10 = 180$
Increase in $\sum x^{2} = 30^{2} - 20^{2} = 900 - 400 = 500$ then
$\sum x^{' 2} = 2830 + 500 = 3330$
Variance $= \frac{1}{n} \sum x^{' 2} - {(\frac{1}{n} \sum x^{'})}^{2}$
$= \frac{1}{15} \times 3330 - {(\frac{1}{15} \times 180)}^{2} = 222 - 144 = 78$

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Q. In an experiment with 15 observation on x, the following results were available

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

, one observation was that + 20 was found to be wrong and was replaced by the correct value 30, then the corrected variance is

In an experiment with 15 observations on $x$ , the 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 $30$ . The corrected variance is

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

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In an experiment with 15 observations on x, the following results were available: ∑x2=2830, ∑x=170 One observation that was 20 was found to be wrong and was replaced by the correct value 30. The corrected variance is:

The correct option is B 78.00 ∑x=170, ∑x2=2830 Increase in ∑x=30−20=10, then ∑x′=170+10=180 Increase in ∑x2=302−202=900−400=500 then ∑x′2=2830+500=3330 Variance =1n∑x′2−(1n∑x′)2 =115×3330−(115×180)2=222−144=78

In an experiment with 15 observations on $x$ , the 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 $30$ . The corrected variance is: