Chapter 12.4, Problem 8P

Make a box and whisker plot to represent each set of data.

Ticket buyers: 220 102 88 98 178 67 42 191 89

To determine

Find minimum , first quartile , median , third quartile , and maximum of the given data set and make a box-and-whisker plot.

Answer to Problem 8P

Minimum = 42

First quartile = 77.5

Median = 98

Third quartile = 184.5

Maximum = 220

Explanation of Solution

Given:

220 , 102 , 88 , 98 , 178 , 67 , 42 , 191 , 89

Calculation:

Arrange the data in ascending order:

42 , 67 , 88 , 89 , 98 , 102 , 178 , 191 , 220

The minimum is 42.

The first quartile is the median of the lower half of the data set.

Since the total entries are 9, which is odd , So, the lower half is the first $\frac{9-1}{2}=4$ entries.

So , the first quartile is $\frac{67+88}{2}=77.5$

Median = The middle entry , since there are 9 entries , which is odd . So, median is the $\frac{9+1}{2}=5^{th}$ entry = 98

The third quartile is the median of the upper half of the data set.

Since the total entries are 9, which is odd , So, the lower half is the last $\frac{9-1}{2}=4$ entries.

So , the third quartile is $\frac{178+191}{2}=184.5$

The maximum is 220