In an experiment with 15 observations, the results are as follows: $\sum x^{2} = 2830, \sum x = 170$ . One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is

78.00

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188.66

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177.33

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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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Similar questions

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

Q. 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:

Q. In an experiment with 15 observations the following results were available

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

. One observation that was

20

was found wrong and was replaced by the correct value

30

. The corrected variance is -

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

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In an experiment with 15 observations, the results are as follows:∑x2=2830, ∑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

The correct option is A 78.00 n=15;∑x2=2830;∑x=170(∑x2) Corrected=2830−(20)2+(30)2=3330(∑x) Corrected=170−20+30=180σ2=333015−(18015)2∴ σ2=∑x2n−(∑xn)2=222−144=78

In an experiment with 15 observations, the results are as follows: $\sum x^{2} = 2830, \sum x = 170$ . One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is