Statistics And Probability Question 428
Question: In an experiment with 15 observations on x, the following results were available $ \sum x^{2}=2830 $ , $ \sum 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
[AIEEE 2003]
Options:
A) 78.00
B) 188.66
C) 177.33
D) 8.33
Show Answer
Answer:
Correct Answer: A
Solution:
$ \sum x=170 $ , $ \sum x^{2}=2830 $ Increase in $ \sum x=10 $ , then $ \sum {x}’=170+10=180 $ Increase in $ \sum x^{2}=900-400=500 $ , then $ \sum {{{x}’}^{2}}=2830+500=3330 $ \ Variance $ =\frac{1}{n}\sum {{{x}’}^{2}}-{{( \frac{\sum {x}’}{n} )}^{2}} $ $ =\frac{3330}{15}-{{( \frac{180}{15} )}^{2}}=222-144=78 $ .
BETA
