Statistics-And-Probability Question 604
Question: In an experiment with 15 observations on X, the following results were available $ \Sigma x^{2}=2830, $ $ \Sigma x=170. $ On observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is
Options:
A) 78.00
B) $ 188.66 $
C) $ 177.33 $
D) $ 8.33 $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Given $ \Sigma x=170,\Sigma x^{2}=2830 $ Increase in $ \Sigma x=10, $ then $ \Sigma x’=170+10=180 $ Increase in $ \Sigma x^{2}=900-400=500, $ then $ \Sigma x{{’}^{2}}=2830+500=3330 $
$ \therefore $ Variance $ =\frac{1}{n}\Sigma x{{’}^{2}}-{{( \frac{\Sigma x’}{n} )}^{2}} $ $ =\frac{3330}{15}-{{( \frac{180}{15} )}^{2}}=222-144=78. $
BETA
