Question

While dividing each entry in a data by a non zero number $a$ the arithmetic mean of the new data

• A. is multiplied by $a$
• B. does not change
• C. is divided by $a$
• D. is diminished by $a$

Answer 1

The correct option is C is divided by $a$

$\text{Let}{x}_1,x_2,x_3,...,x_n\text{be n items.}$
$\text{Then their arithmetic mean is}$
$\overline{x}=\frac{x_1+x_2+x_3+...+x_n}{n}$
$\text{After dividing each entries with 'a', the items becomes}$
$\frac{x_1}{a},\frac{x_2}{a},\frac{x_3}{a},...,\frac{x_n}{a}$
$\text{Then their arithmetic mean is}$
$A.M=\frac{\frac{x_1}{a}+\frac{x_2}{a}+\frac{x_3}{a}+...+\frac{x_n}{a}}{n}$
$=\frac{1}{a}\left(\frac{x_1+x_2+x_3+...+x_n}{n}\right)$
$=\frac{1}{a}\left(\overline{x}\right)$
$\text{Therefore on dividing each entry by 'a' the AM means is also divided by a}$
Option C is correct.