Chapter 12.4, Problem 9P

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

Marathon race finishers: 3,869 3,981 3,764 3,786, 4,310 3,993 3,258

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 9P

Minimum = 3258

First quartile = 3764

Median = 3869

Third quartile = 3993

Maximum = 4310

Explanation of Solution

Given:

3869 , 3981 , 3764 , 3786 , 4310 , 3993 , 3258

Calculation:

Arrange the data in ascending order:

3258 , 3764 , 3786 , 3869 , 3981 , 3993 , 4310

The minimum is 3258.

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

Since the total entries are 7, which is odd , So, the lower half is the first $\frac{7-1}{2}=3$ entries.

So , the first quartile is $3764$

Median = The middle entry , since there are 7 entries , which is odd . So, median is the $\frac{7+1}{2}=4^{th}$ entry = 3869

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

Since the total entries are 7, which is odd , So, the lower half is the last $\frac{7-1}{2}=3$ entries.

So , the third quartile is 3993

The maximum is 4310