Statistics And Probability Question 77
Question: Let $ x_1,,x_2,….,x_{n} $ be n observations such that $ \sum x_i^{2}=400 $ and $ \sum x_i^{{}}=80 $ . Then a possible value of n among the following is
[AIEEE 2005]
Options:
A) 9
B) 12
C) 15
D) 18
Show Answer
Answer:
Correct Answer: D
Solution:
Since, root mean square ³ arithmetic mean \ $ \sqrt{\frac{\sum\limits_{i=1}^{n}{x_i^{2}}}{n}}\ge \frac{\sum\limits_{i=1}^{n}{x_{i}}}{n}=\sqrt{\frac{400}{n}}\ge \frac{80}{n}\Rightarrow n\ge 16 $ Hence, possible value of n = 18.
BETA
