Question

Calculate the interquartile range of the following data: 17, 18, 18, 19, 20, 21, 21, 23, 25

Answer 1

To find the interquartile range, we first need to find the median of the data set.

Median:

Arrange the data in order from smallest to largest:

17, 18, 18, 19, 20, 21, 21, 23, 25

The median is the middle number. Since there are 9 numbers in the set, the middle number is the 5th number.

Median = 20

Next, we need to find the median of the lower half of the data set (the numbers below the median).

Lower Half:

17, 18, 18, 19

The median of the lower half is the middle number. Since there are 4 numbers in the lower half, the middle number is the 2nd number.

Median of Lower Half = 18

Finally, we need to find the median of the upper half of the data set (the numbers above the median).

Upper Half:

21, 21, 23, 25

The median of the upper half is the middle number. Since there are 4 numbers in the upper half, the middle number is the 2nd number.

Median of Upper Half = 22

Now we have the first quartile (Q1) as the median of the lower half and the third quartile (Q3) as the median of the upper half.

Q1 = 18

Q3 = 22

Finally, we can calculate the interquartile range (IQR) by subtracting Q1 from Q3.

IQR = Q3 - Q1

IQR = 22 - 18

IQR = 4

Therefore, the interquartile range of the given data set is 4.