Question

Using the following set of data, calculate the lower quartile, the upper quartile, and the interquartile range.20, 22, 25, 28, 29, 30, 32, 33, 34
Be sure to show your work for finding:
The lower quartile
The upper quartile
The interquartile range

Answer 1

Answer:

The lower quartile is 23.5

The upper quartile is 32.5

The interquartile range is 9

Step-by-step explanation:

The given data set is 20, 22, 25, 28, 29, 30, 32, 33, 34.

The data set is already sorted in ascending order.

The middle number of this data set is called the median.

Therefore the median is 29.

The median divides the data set into two halves.

The lower half is

20, 22, 25, 28

The median of the lower half is the lower quartile.

$Q_1 = \frac{22 + 25}{2} = \frac{47}{2} = 23.5$

The upper half is 30, 32, 33, 34

The median of the upper half is the upper quartile.

$Q_3= \frac{33 + 32}{2} = 32.5$

The interquartile range is given by

$IQR=Q_3-Q_1 \\ IQR=32.5 - 23.5 = 9$