Chapter 12.4, Problem 11P

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

Ticket prices: $25.50 $ 45 $24 $32.50 $32 $20 $38.50 $50 $45

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 11P

Minimum = 20

First quartile = 24.75

Median = 32.50

Third quartile = 45

Maximum = 50

Explanation of Solution

Given:

25.50 , 45 , 24 , 32.50 , 32 , 20 , 38.50 , 50 , 45

Calculation: ,

Arrange the data in ascending order:

20 , 24 , 25.50 , 32 , 32.50 , 38.50 , 45 , 45 , 50

The minimum is 20.

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 $\frac{24+25.50}{2}=24.75$

Median = The middle quantity as the number of entries is 9 , which is odd = $\frac{9+1}{2}=5^{th}$ entry = 32.50

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

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

So , the third quartile is $\frac{45+45}{2}=45$

The maximum is 50