Statistics And Probability Question 274
Question: The mean of 100 observations is 50 and their standard deviation is 5. The sum of squares of all the observations is
Options:
A) 50000
B) 250000
C) 252500
D) 255000
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Given, $ \bar{x}=50,n=100 $ and $ \Sigma =5 $ $ \Sigma ,50=\frac{\Sigma ,x_{i}}{100} $
$ \Rightarrow \Sigma ,x_{i}=50\times 100=5000 $ Now, $ {{\Sigma }^{2}}=\frac{\Sigma ,x_i^{2}}{n}-{{(\bar{x})}^{2}} $
$ \Rightarrow 25=\frac{\Sigma ,x_i^{2}}{100}-{{(50)}^{2}} $
$ \Rightarrow 2525=\frac{\Sigma ,x_i^{2}}{100} $
$ \therefore ,\Sigma ,x_i^{2}=252500 $
BETA
