Question

A sequence consists of $7$ terms arranged in descending order. Then mean value of the sequence is $70.$ If $30$ is added to each term and then each term is divided by $2$, then

• A. the absolute value of difference between new mean and old mean is $15$
• B. the absolute value of difference between new mean and old mean is $20$
• C. the absolute value of difference between new mean and old mean is $0$
• D. the position of new median will not change.

Answer 1

Answer: (B), (D)

the position of new median will not change.

The Mean of $7$ data $\overline{x}=70$
now $30$ is added and divided by $2$ then new mean is
New mean $=(\overline{x}+30)\times \frac{1}{2}$
$=(70+30)\times \frac{1}{2}$
$=50$
Now absolute value of difference of means is $|50-70|=20$

Since all the terms has been added with $30$ and then divided by $2$, therefore the position of median (middle term) will not change.