Question

The number of people participated in a Marathon race at various places is given.


If 20 partipants are exited from each places, what change in the median can be observed?

• A. It will increase
• B. It will decrease
• C. I will be equal
• D. It will double the original value.

Answer 1

The correct option is B It will decrease

The given data set is

830, 767, 838, 706, 400, 780

Arrange the numbers in ascending order, we get

400, 706, 767, 780, 830, 838

For a set with an even number of values, the median is the mean of the two middle values.

Median = $\frac{767+780}{2}$

= $\frac{1547}{2}$

= 773.5

$\therefore$ Median = 773.5

Each data in the data set is decreased by 20.

Hence, the new data set is

830-20, 767-20, 838-20, 706-20, 400-20, 780-20

= 810, 747, 818, 686, 380, 760

Arranging the new data in ascending order, we get

380, 686, 747, 760, 810, 818

Here, the middle values are 747, 760.

New median = $\frac{747+760}{2}$

= 753.5

$\because$ The new median is less than the old median.

Hence, the median decreases.