Statistics And Probability Question 374
Question: If $ \sum\nolimits_{i=1}^{9}{(x_{i}-5)=9} $ and $ \sum\nolimits_{i=1}^{9}{{{(x_{i}-5)}^{2}}=45,} $ then the standard deviation of the 9 items $ x_1,x_2,…x_9 $ is
Options:
A) 9
B) 4
C) 3
D) 2
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Let $ \sum\limits_{i=1}^{9}{(x_{i}-5)}=9\Rightarrow \sum\limits_{i=1}^{9}{x_{i}-\sum\limits_{i=1}^{9}{5=9}} $
$ \Rightarrow \sum\limits_{i=1}^{9}{x_{i}-(9\times 5)=9;} $ $ \sum{x_{i}-45=\Rightarrow \sum{x_{i}=54}} $ Similarly, $ \sum{x_i^{2}-10\times 54+25\times 9=45\Rightarrow \sum{x_i^{2}=360}} $
$ \Rightarrow \sigma =\sqrt{\frac{360}{9}-{{( \frac{54}{9} )}^{2}}}=\sqrt{\frac{324}{81}}=2 $
BETA
