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 |

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

Median profit of the company = $15 millions

Correct answer : (3)

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 |

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

Middle quartile = Median of all the data

=

[Simplify.]

Lower quartile = Median of lower half of the data

=

[Simplify.]

Upper quartile = Median of upper half of the data

=

[Simplify.]

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

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

Correct answer : (1)

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 |

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

Middle quartile = median of the entire data = 18

=

Lower quartile = median of lower half of the data

[Simplify.]

=

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.]

Correct answer : (3)

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 |

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.

Correct answer : (4)

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 |

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 =

Correct answer : (1)

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 |

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 =

[Simplify.]

Upper quartile = Median of upper half of the data =

[Simplify.]

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

Mean number of T.V viewers =

=

[Substitute and simplify.]

Correct answer : (4)

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 |

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.

Correct answer : (2)

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 |

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.

Correct answer : (3)

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. | $\frac{1}{2}$ |

The middle quartile of the plot = 12

So, the ratio of the least value to the middle quartile is

[Simplify.]

Correct answer : (3)

10.

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

a. | 10 | ||

b. | 50 | ||

c. | 45 | ||

d. | 65 |

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

So, the outlier in the plot is 10.

Correct answer : (1)