Statistics-And-Probability Question 603
Question: If the arithmetic mean of the numbers $ x_1,x_2,x_3,…x_{n} $ is $ \bar{x} $ . Then the arithmetic mean of numbers $ ax_1+b,ax_2+b,ax_3+b,…ax_{n}+b, $ Where a, b are two constants would be
Options:
A) $ \bar{x} $
B) $ na\bar{x}+nb $
C) $ a\bar{x} $
D) $ a\bar{x}+b $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Required mean $ =\frac{(ax_1+b)+(ax_2+b)+…+(ax_{n}+b)}{n} $ $ =\frac{a(x_1+x_2+…+x_{n})+nb}{n}=a\bar{x}+b, $ $ ( \because \frac{x_1+x_2+…+x_{n}}{n}=\bar{x} ). $
BETA
