Statistics-And-Probability Question 637
Question: The variance of first 50 even natural numbers is
Options:
A) 437
B) $ \frac{437}{4} $
C) $ \frac{833}{4} $
D) $ 833 $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] First 50 even natural numbers are 2, 4, 6?,100 Variance $ =\frac{\sum{x_i^{2}}}{N}-{{(\bar{x})}^{2}} $
$ \Rightarrow {{\sigma }^{2}}=\frac{2^{2}+4^{2}+…+100^{2}}{50}-{{( \frac{2+4+…+100}{50} )}^{2}} $ $ =\frac{4(1^{2}+2^{2}+3^{2}+…+50^{2})}{50}-{{(51)}^{2}} $ $ =4( \frac{50\times 51\times 101}{50\times 6} )-{{(51)}^{2}}=3434-2601 $
$ \Rightarrow {{\sigma }^{2}}=833 $
BETA
