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 :  $\mathrm{\Sigma }{x}^{2}=2830,\mathrm{\Sigma }x=170$One observation that was $20$ was found wrong and was replaced by the correct value $30.$ The corrected variance is

1. A

$8.33$

2. B

$78.00$

3. C

$188.66$

4. D

$177.33$

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### Solution:

We have,

Corrected $\mathrm{\Sigma }{x}^{2}=2830-{20}^{2}+{30}^{2}=3330$

Corrected $\mathrm{\Sigma }x=170-20+30=180$

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

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