#### Solved Examples and Worksheet for Constructing Box-and-Whisker Plots

Q1The table shows the percentage of scores obtained by John 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

Step: 1
The ascending order of the percentages obtained by John is 70, 76, 80, 82.
Step: 2
In the percentages, the least value is 70 and the greatest value is 82.
Step: 3
Middle quartile = Median of all the data
Step: 4
= 76 + 802 = 1562 = 78
Step: 5
Lower quartile = Median of lower half of the data
Step: 6
= 70 + 762 = 1462 = 73
Step: 7
Upper quartile = Median of upper half of the data
Step: 8
= 80 + 822 = 1622 = 81
Step: 9
So, plot (1) is the equivalent box-and-whisker plot of the data.
Step: 10
Median of the scores obtained by John = Middle quartile = 78
Correct Answer is :   Plot 1, 78
Q2TJoseph, John, table shows tJoseph, John, number of coins collected by 5 students. Which of tJoseph, John, following is tJoseph, John, equivalent box-and-whisker plot for tJoseph, John, table? Also find out tJoseph, John, range of tJoseph, John, box-and-whisker plot.
 Students Number of coins Joseph, John,name 18 Charles 10 CatJoseph, John,rine 16 Cindy 20 Jack 16 A. Plot 3, 10
B. Plot 2, 18
C. Plot 4, 30
D. Plot 1, 10

Step: 1
TJoseph, John, ascending order of tJoseph, John, number of coins collected by each student is 10, 16, 16, 18, 20.
Step: 2
In tJoseph, John, table, least value is 10 and tJoseph, John, greatest value is 20.
Step: 3
Middle quartile = median of tJoseph, John, entire data = 16
Step: 4
Lower quartile = median of lower half of tJoseph, John, data
= 10 + 162 = 262 = 13
Step: 5
Upper quartile = Median of upper half of tJoseph, John, data
= 18 + 202 = 382 = 19
Step: 6
Plot (1) is tJoseph, John, equivalent box-and-whisker plot for tJoseph, John, data.
Step: 7
Range of tJoseph, John, box-and-whisker plot
= Greatest value - Least value

Step: 8
= 20 - 10 = 10.
[Substitute and subtract.]
Correct Answer is :   Plot 1, 10
Q3The owner of a super market recorded the number of customers who visited his store each hour on a particular day. The results were 15, 10, 12, 9, 18, 5, 8, 9, 15, 10, and 11. Which box-and-whisker plot matches the data? A. Plot 1
B. Plot 2
C. Plot 3
D. Plot 4

Step: 1
The number of customers who visited the super market each hour are 15, 10, 12, 9, 18, 5, 8, 9, 15, 10 and 11.
Step: 2
The ascending order of the above data set is: 5, 8, 9, 9, 10, 10, 11, 12, 15, 15,18.
Step: 3
The least value in the above list of data is 5 and the greatest value is 18.
Step: 4
Middle quartile = median of the data = 10.
Step: 5
Lower quartile = median of lower half of the data = 9.
Step: 6
Upper quartile = median of upper half of the data = 15.
Step: 7
So, among the plots, plot 4 is the equivalent box-and-whisker plot for the data.
Correct Answer is :   Plot 4
Q4The table shows the different editions of the famous novel 'Harry Potter' and the income received. Which box-and-whisker plot matches the data shown in the table?
 Edition Income (Million dollars) Harry Potter and the Sorcerer's stone 10 Harry Potter and the Chamber of Secrets 40 Harry Potter and the Prisoner of Azkaban 80 Harry Potter and the Goblet of Fire 150 Harry Potter and the order of the Phoenix 200 A. Plot 1
B. Plot 2
C. Plot 3
D. Plot 4

Step: 1
The least value in the above list of data = 10 and the greatest value = 200.
Step: 2
Middle quartile = median of all the data = 80.
Step: 3
Lower quartile = median of lower half of the data = 10 + 402 = 502 = 25
Step: 4
Upper quartile = median of upper half of the data = 150 + 2002 = 3502 = 175
Step: 5
So, plot 3 is the equivalent box-and-whiskers plot for the data.
Correct Answer is :   Plot 3
Q5There is a bus transporting passengers between two places A and B. The number of passengers transported in 7 trips in a day are recorded as 50, 70, 60, 80, 40, 75, 50. Choose the appropriate box-and-whisker plot of the data and find the median of the data. A. Plot 1, 20
B. Plot 4, 80
C. Plot 3, 20
D. Plot 2, 60

Step: 1
The number of passengers transported in 7 trips in a day are 50, 70, 60, 80, 40, 75, 50.
Step: 2
The ascending order of the above data set is 40, 50, 50, 60, 70, 75 and 80.
Step: 3
The least value in the above list is 40 and the greatest value is 80.
Step: 4
Middle quartile = median of the data = 60.
Step: 5
Lower quartile = median of lower half of the data = 50.
Step: 6
Upper quartile = median of upper half of the data = 75.
Step: 7
Plot (2) is the appropriate box-and-whisker plot of the data.
Step: 8
Median of the data = middle quartile of the plot = 60
Correct Answer is :   Plot 2, 60
Q6The table shows the heights of mountains in the U.S. Choose the appropriate box-and-whisker plot of the data and find the mean height of the mountains in the 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

Step: 1
From the table, the heights of mountains in the U.S are 200, 180, 175, 165, 160, 145 and 140.
Step: 2
The ascending order of the above data set is 140, 145, 160, 165, 175, 180, 200.
Step: 3
So, the least value in the data set is 140 and the greatest value is 200.
Step: 4
Middle quartile = median of the data = 165.
Step: 5
Lower quartile = median of lower half of the data = 145
Step: 6
Upper quartile = median of upper half of the data = 180
Step: 7
So, plot (1) is the appropriate box-and-whisker plot of the data.
Step: 8
Mean of the data = sum of the heights / number of heights given = [(140 + 145 + 160 + 165 + 175 + 180 + 200) / 7] x 100 = 166.43 x 100 = 16643 ft.
Correct Answer is :   Plot 1, 16643 ft
Q7The table shows the number of viewers of different TV channels in the U.S. Choose the appropriate box-and-whisker plot for the data and find the mean number of TV viewers.
Number of viewers of different TV 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

Step: 1
The ascending order of the number of viewers in the data is 10, 14, 16, 20 and 32.
Step: 2
The least value in the above list is 10 and the greatest value is 32.
Step: 3
Middle quartile of the plot = Median of the given data = 16

Step: 4
Lower quartile = Median of lower half of the data = 10+142 = 242 = 12
[Simplify.]
Step: 5
Upper quartile = Median of upper half of the data = 20+322 = 522 = 26
[Simplify.]
Step: 6
Among the plots, plot (4) is the appropriate box-and-whisker plot for the data.
Step: 7
Mean number of T.V viewers = Sum of the viewers of all channels / Number of channels
Step: 8
= 10+14+16+20+325 = 18.4 millions
[Substitute and simplify.]
Correct Answer is :   Plot 4, 18.4 millions
Q8Choose the appropriate box-and-whisker plot of the given 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

Step: 1
The ascending order of the data is 2, 2, 3, 4, 5, 5, 7, 8, 9, 10 and 12.
Step: 2
The least value in the data set is 2 and the greatest value is 12.
Step: 3
Middle quartile = Median of the data = 5

Step: 4
Lower quartile = Median of lower half of the data = 3

Step: 5
Upper quartile = Median of upper half of the data = 9

Step: 6
So, Plot 3 is the appropriate box-and-whisker plot for the data set.
Correct Answer is :   Plot 3
Q9The table shows the number of different colored balls in a box. Pick an appropriate box-and-whisker plot that describes the data.
Different colors of balls in a box
 Color Number of balls Red 7 Blue 8 Green 6 White 3 Black 10 Yellow 5 Pink 2 A. Plot 1
B. Plot 2
C. Plot 3
D. Plot 4

Step: 1
The ascending order of the above data set is 2, 3, 5, 6, 7, 8 and 10.
Step: 2
From the above data set, the least value is 2 and the greatest value is 10.
Step: 3
Middle quartile = Median of the whole data set = 6

Step: 4
Lower quartile = Median of lower half of the data set = 3

Step: 5
Upper quartile = Median of upper half of the data set = 8

Step: 6
Among the four plots, plot (2) is the equivalent box-and-whisker plot of the data.
Correct Answer is :   Plot 2
Q10The number of students in Grade 7 at 15 schools in New York are recorded as 15, 8, 10, 11, 13, 17, 19, 20, 18, 12, 14, 18, 17, 19 and 20. Find the range of the data and pick the appropriate box-and-whisker plot of the data. A. Plot 1, 20
B. Plot 2, 12
C. Plot 3, 8
D. Plot 4, 17

Step: 1
Range = greatest value - least value.
Step: 2
The ascending order of the above data set is: 8, 10, 11, 12, 13, 14, 15, 17, 17, 18, 18, 19, 19, 20, 20.
Step: 3
From the above list of data, least value = 8 and greatest value = 20.
Step: 4
The range of the data = 20 - 8 = 12
Step: 5
Middle quartile = median of all the data set = 17.
Step: 6
Lower quartile = median of lower half of the data set = 12.
Step: 7
Upper quartile = median of upper half of the data set = 19.
Step: 8
Among the four plots, plot (2) is the appropriate box-and-whisker plot of the data.
Correct Answer is :   Plot 2, 12