Chapter 12.4, Problem 12P

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

Head circumference (cm): 60.5 54.5 55 57.5 59 58.5 57 56.75 57

To determine

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

Answer to Problem 12P

Minimum = 54.5

First quartile = 56.75

Median = 57.25

Third quartile = 58.5

Maximum = 60.5

Explanation of Solution

Given:

60.5 , 54.5 , 55 , 57.5 , 59 , 58.5 , 58.5 , 57 , 56.75 , 57

Calculation:

Arrange the data in ascending order:

54.5 , 55 , 56.75 , 57 , 57 , 57.5 , 58.5 , 58.5 , 59 , 60.5

The minimum is 54.5.

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

Since the total entries are 10, which is even , So, the lower half is the first $\frac{10}{2}=5$ entries.

So , the first quartile is 56.75

Median = The mean of $\frac{10}{2}=5^{th}\&6^{th}$ entry = $\frac{57+57.5}{2}=57.25$

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

Since the total entries are 10, which is even , So, the upper half is the last $\frac{10}{2}=5$ entries.

So , the third quartile is 58.5

The maximum is 60.5