Question

A family of bears is going to a movie. The following data points represent the ticket and candy price (in dollars) for each bear. Find the interquartile range (IQR) of the data set.

0, 1 1/2, 2 1/2, 3, 4, 4, 4, 7, 7 1/2

Answer 1

The interquartile range (IQR) of the data set is:

3.5

Explanation:

The data points are given as follows:

0, 1 1/2, 2 1/2, 3, 4, 4, 4, 7, 7 1/2

i.e. 0 , 1.5 , 2.5 , 3 , 4 , 4 , 4 , 7 , 7.5

There are a total of 9 data points and we know that the median of the data is the central tendency of the data and it always exist in the middle of the data.

Here we have 9 data points.

and hence the median exist at the the 5th place.

Hence, Median of data of Middle quartile i.e.
`Q_2`= 4

• Also, the lower set of data is:

0 , 1.5 , 2.5 , 3

and the first quartile or the lower quartile i.e.
`Q_1` is the median of the lower set of data.

i.e.
`Q_1=(1.5+2.5)/(2)\\\\i.e.\\\\Q_1=2`

• The upper set of data is:

4 , 4 , 7 , 7.5

and the third quartile or the upper quartile i.e.
`Q_3` is the median of the upper set of data.

i.e.
`Q_3=(4+7)/(2)\\\\i.e.\\\\Q_3=5.5`

Hence, the interquartile range (IQR) of the data set is given by:

`IQR=Q_3-Q_1\\\\i.e.\\\\IQR=5.5-2\\\\i.e.\\\\IQR=3.5`