Statistics And Probability Question 319
Question: Suppose a population A has 100 observations $ 101,102,…..,200 $ and another population B has 100 observations 151, 152, …, 250. If $ V_{A}andV_{B} $ represent the variances of the two populations, respectively then $ \frac{V_{A}}{V_{B}} $ is
Options:
1
B) $ \frac{9}{4} $
C) $ \frac{4}{9} $
D) $ \frac{2}{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \sigma _x^{2}=\frac{\sum{(x_i - \bar{x})^2}}{n} $
(Here deviations are taken from the mean). Since A and B both have 100 consecutive integers, they therefore have the same standard deviation and hence the variance.
$ \therefore \frac{V_{A}}{V_{B}}=1 $
(As $ \sum{d_i^{2}} $ is same in both the cases)
BETA
