# Box and Whisker Plots Worksheet

Box and Whisker Plots Worksheet
• Page 1
1.
The box-and-whisker plot describes the profits of a software company(in million dollars) during the last ten years. What is the median profit of the company from the plot?

 a. $25 millions b.$10 millions c. $15 millions d.$20 millions

#### Solution:

Median of the data is equal to the middle quartile value in its equivalent box-and-whisker plot.

From the box-and-whisker plot, middle quartile value = 15

Median profit of the company = \$15 millions

2.
The table shows the percentage of scores obtained by Ethan each year during his four year degree course. Which of the following is the equivalent box-and-whisker plot of the data? Also find out the median of scores obtained.
 Year Percentage of scores 1st Year 70 2nd Year 82 3rd Year 76 4th Year 80

 a. Plot 1, 78 b. Plot 2, 90 c. Plot 3, 60 d. Plot 4, 80

#### Solution:

The ascending order of the percentages obtained by Ethan is 70, 76, 80, 82.

In the percentages, the least value is 70 and the greatest value is 82.

Middle quartile = Median of all the data

= (76+80)2 = 1562 = 78
[Simplify.]

Lower quartile = Median of lower half of the data

= (70+76)2 = 1462 = 73
[Simplify.]

Upper quartile = Median of upper half of the data

= (80+82)2 = 1622 = 81
[Simplify.]

So, plot (1) is the equivalent box-and-whisker plot of the data.

Median of the scores obtained by Ethan = Middle quartile = 78

3.
The table shows the scoreboard of a 100 meters running race. Which of the following is the equivalent box-and-whisker plot for the table? Also find out the range of the box-and-whisker plot.
 Contestant Time taken (in seconds) Tom 20 Jerry 18 Ben 14 Lee 10 Peter 18

 a. Plot 1, 20 b. Plot 2, 18 c. Plot 3, 10 d. Plot 4, 30

#### Solution:

The ascending order of the times taken by each contestant to complete tha race (in seconds) is 10, 14, 18, 18 and 20.

In the table, least value is 10 and the greatest value is 20.

Middle quartile = median of the entire data = 18

= (10+14)2 = 242 = 12
Lower quartile = median of lower half of the data
[Simplify.]

= (18+20)2 = 382 = 19
Upper quartile = Median of upper half of the data
[Simplify.]

Plot (3) is the equivalent box-and-whisker plot for the data.

= Greatest value - Least value
Range of the box-and-whisker plot

= 20 - 10 = 10 seconds
[Substitute and simplify.]

4.
The owner of a super market recorded the number of customers who came into his store each hour for one day. The results were 15, 10, 12, 9, 18, 5, 8, 9, 15, 10 and 11. Which of the four plots is the suitable box-and-whisker plot of the data?

 a. Plot 1 b. Plot 2 c. Plot 3 d. Plot 4

#### Solution:

The number of customers who visited the super market each hour are 15, 10, 12, 9, 18, 5, 8, 9, 15, 10 and 11.

The ascending order of the above data set is: 5, 8, 9, 9, 10, 10, 11, 12, 15, 15,18.

The least value in the above list of data is 5 and the greatest value is 18.

Middle quartile = median of the data = 10.

Lower quartile = median of lower half of the data = 9.

Upper quartile = median of upper half of the data = 15.

So, among the plots, plot 4 is the equivalent box-and-whisker plot for the data.

5.
The table shows the heights of mountains in U.S. Choose the appropriate box-and-whisker plot of the data and find the mean height of the mountains in U.S.
 Name Height (in 100 ft.) Mt. McKinley 200 Mt. St. Elias 180 Mt. Foraker 175 Mt. Bona 165 Mt. Blackburn 160 Mt. Alverstone 145 Sunshine Peak 140

 a. Plot 1, 16643 ft b. Plot 2, 14000 ft c. Plot 3, 17732 ft d. Plot 4, 16500 ft

#### Solution:

From the table, the heights of mountains in the U.S are 200, 180, 175, 165, 160, 145 and 140.

The ascending order of the above data set is 140, 145, 160, 165, 175, 180, 200.

So, the least value in the data set is 140 and the greatest value is 200.

Middle quartile = median of the data = 165.

Lower quartile = median of lower half of the data = 145

Upper quartile = median of upper half of the data = 180

So, plot (1) is the appropriate box-and-whisker plot of the data.

Mean of the data = Sum of the heightsNumber of heights given = 140 + 145 + 160 + 165 + 175 + 180 + 2007 × 100 = 166.43 × 100 = 16643 ft.

6.
The table shows the number of viewers of different T.V channels in U.S.A. Choose the appropriate box-and-whisker plot for the data and find the mean number of T.V viewers.
Number of viewers of different T.V channels in U.S
 Channel Number of viewers (in millions) Discovery 20 Star Sports 10 Star Movies 32 Cartoon Network 16 CNN 14

 a. Plot 1, 16 millions b. Plot 2, 32.3 millions c. Plot 3, 10.5 millions d. Plot 4, 18.4 millions

#### Solution:

The ascending order of the number of viewers in the data is 10, 14, 16, 20 and 32.

The least value in the above list is 10 and the greatest value is 32.

Middle quartile of the plot = Median of the given data = 16

Lower quartile = Median of lower half of the data = 10+14 / 2 = 24 / 2 = 12
[Simplify.]

Upper quartile = Median of upper half of the data = 20+32 / 2 = 52 / 2 = 26
[Simplify.]

Among the plots, plot (4) is the appropriate box-and-whisker plot for the data.

Mean number of T.V viewers = Sum of the viewers of all channelsNumber of channels.

= 10+14+16+20+32 / 5 = 18.4 millions
[Substitute and simplify.]

7.
Choose the appropriate box-and-whisker plot of the data set. 2, 2, 3, 5, 9, 8, 4, 7, 10, 5 and 12

 a. Plot 1 b. Plot 2 c. Plot 3 d. Plot 4

#### Solution:

The ascending order of the data is 2, 2, 3, 4, 5, 5, 7, 8, 9, 10 and 12.

The least value in the data set is 2 and the greatest value is 12.

Middle quartile = Median of the data = 5

Lower quartile = Median of lower half of the data = 3

Upper quartile = Median of upper half of the data = 9

So, Plot 2 is the appropriate box-and-whisker plot for the data set.

8.
The box-and-whisker plot shows number of books sold per day in a month. Find out the lower quartile of the box-and-whisker plot.

 a. 52 b. 53 c. 48 d. 46

#### Solution:

The lower quartile is the median of the data values from least value to the middle quartile.

The box in a box-and-whisker plot always starts from the lower quartile value.

The lower quartile of the box-and-whisker plot = 48.

9.
The number of letters in each student's name in a school is given in the box-and-whisker plot. What is the ratio of the least value of the plot to the middle quartile of the plot?

 a. $\frac{1}{3}$ b. $\frac{4}{3}$ c. $\frac{2}{3}$ d. $\frac{1}{2}$

#### Solution:

From the given plot, the least value = 8

The middle quartile of the plot = 12

So, the ratio of the least value to the middle quartile is 8 / 12 = 2 / 3.
[Simplify.]

10.
What is the outlier in the box-and-whisker plot?

 a. 10 b. 50 c. 45 d. 65

#### Solution:

The outlier in a box-and-whisker plot is the data item, which is much higher or much lower than the other set of data items.

In the plot, the number 10 is much farther from the remaining set of data items.

So, the outlier in the plot is 10.