Question

If each entry of a data is decreased by $8$, what is the change in the arithmetic mean?

• A. Remains the same
• B. Decreases by $8$
• C. Increases by $8$
• D. Can't be determined

Answer 1

The correct option is B Decreases by $8$

Let the mean be $x$ and number of data be $n$

$\therefore$ Sum of data $=xn$

After decreasing 8 from each data, Sum $=xn-8n$

$\therefore$ New mean $=\frac{xn-8n}{n}=x-8$

$\therefore$ New mean is decreased by 8

$(Ans\to B)$