Question

Case study

Answer 1

Given:

The data set is

21, 16, 30, 15, 16, 18, 10, 24, 26, 20, 19, 24, 24, 25, 23

10, 15, 16, 16, 18, 19, 20, 21, 23, 24, 24, 24, 25, 26, 30

To find:

The range, average and median for the given data set.

Solution:

Arrange the data set in ascending order.

10, 15, 16, 16, 18, 19, 20, 21, 23, 24, 24, 24, 25, 26, 30

(1)

Range = Maximum value - Minimum value

           = 30 - 10

           = 20

Therefore, the range of the given data set is 20. All the options are incorrect.

(2)

$Average=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}$

$Average=\dfrac{311}{15}$

$Average\approx 20.73$

Therefore, the average score is about 20.73. All the options are incorrect.

(3)

Number of observations = 15, which is odd.

$Median=\dfrac{n+1}{2}\text{th term}$

$Median=\dfrac{15+1}{2}\text{th term}$

$Median=\dfrac{16}{2}\text{th term}$

$Median=8\text{th term}$

In the arranged data set 8th term is 21.

$Median=21$

Therefore, the correct option is b.