Statistics And Probability Question 510
Question: Let $ x_1,x_2,x_3,x_4 $ and $ x_5 $ be the observations with mean m and standard deviation s. The standard deviation of the observations $ kx_1, $ $ kx_2, $ $ kx_3, $ $ kx_4, $ and $ kx_5, $ is
Options:
A) $ k+s $
B) s/k
C) ks
D) s
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Here, $ m=\frac{\Sigma x_{i}}{5},,s=\sqrt{\frac{\Sigma x_i^{2}}{5}-{{( \frac{\Sigma x_{i}}{5} )}^{2}}} $ For observations $ kx_1,kx_2,kx_3,kx_4,kx_5, $ $ SD=\sqrt{\frac{k^{2}\Sigma x_i^{2}}{5}-{{( \frac{k\Sigma x_{i}}{5} )}^{2}}} $ $ =\sqrt{\frac{k^{2}\Sigma x_i^{2}}{5}-k^{2}{{( \frac{\Sigma x_{i}}{5} )}^{2}}} $ $ =k\sqrt{\frac{\Sigma x_i^{2}}{5}-{{( \frac{\Sigma x_{i}}{5} )}^{2}}}=ks $
BETA
