Statistics And Probability Question 496
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) $ n,a\bar{x}+nb $
C) $ a\bar{x} $
D) $ a\bar{x}+b $
Show Answer
Answer:
Correct Answer: D
Solution:
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
