Statistics And Probability Question 355
Question: Let $ x_1,x_2,…x_{n} $ be n observations such that $ \sum{x_i^{2}=400} $ and $ \sum{x_{i}=80.} $ Then the possible value of n among the following is
Options:
A) 15
B) 18
C) 9
D) 12
Show Answer
Answer:
Correct Answer: B
Solution:
[b] We know that for positive real numbers $ x_1, $ $ x_2,…,x_{n}, $ We have $ \frac{\sum{x_i^{2}}}{n}\ge {{( \frac{\sum{x_{i}}}{n} )}^{2}}\Rightarrow \frac{400}{n}\ge {{( \frac{80}{n} )}^{2}} $
$ \Rightarrow n\ge 16. $ so only possible value of n=18
BETA
