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Box & Whisker Plot Worksheet
Practice Problems
From the box-and-whisker plot, middle quartile value = 15
Median profit of the company = $15 millions
In the percentages, the least value is 70 and the greatest value is 82.
Middle quartile = Median of all the data
=7 6 + 8 0 2 156 2
[Add and simplify.]
Lower quartile = Median of lower half of the data
=7 0 + 7 6 2 146 2
[Add and simplify.]
Upper quartile = Median of upper half of the data
=8 0 + 8 2 2 162 2
[Add and simplify.]
So, plot (1) is the equivalent box-and-whisker plot of the data.
Median of the scores obtained by John = Middle quartile = 78
In the table, least value is 10 and the greatest value is 20.
Middle quartile = median of the entire data = 16
=1 0 + 1 6 2 26 2
Lower quartile = median of lower half of the data
[Add and simplify.]
=1 8 + 2 0 2 38 2
Upper quartile = Median of upper half of the data
[Add and simplify.]
Plot (1) is the equivalent box-and-whisker plot for the data.
= Greatest value - Least value
Range of the box-and-whisker plot
= 20 - 10 = 10.
[Substitute and subtract.]
Range = Greatest value - Least value
= $200 - $75 = $125
[Substitute and subtract.]
Range of the earnings = $125
From the plot average median speed of Car B is greater than Car A.
From the plot maximum height of the girls is fairly close to the maximum height of the boys.
From the plot, range of Worker A is 250 - 100 = 150.
From the plot, range of Worker B is 200 - 75 = 125.
Range of Worker A is greater than the range of Worker B.
From the given box and whisker plot, the upper quartile is 37.5 and the lower quartile is 12.5.
= 37.5 - 12.5 = 25
Interquartile range = upper quartile - lower quartile
So, the interquartile range for the given box and whisker plot is 25.
From the given box and whisker plot, the upper quartile is 300 and the lower quartile is 100.
= 300 - 100 = 200
Interquartile range = upper quartile - lower quartile
So, the interquartile range for the given box and whisker plot is 200.
Box & Whisker Plot Worksheet
- Page 1
1.
The box-and-whisker plot shows the profits of a software company (in million dollars) in the last ten years. Find the median profit of the company.
| a. | $25 millions | ||
| b. | $20 millions | ||
| c. | $10 millions | ||
 | d. | $15 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
Correct answer : (4)
2.
The 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 |
Solution:
The ascending order of the percentages obtained by John 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
=
[Add and simplify.]
Lower quartile = Median of lower half of the data
=
[Add and simplify.]
Upper quartile = Median of upper half of the data
=
[Add and simplify.]
So, plot (1) is the equivalent box-and-whisker plot of the data.
Median of the scores obtained by John = Middle quartile = 78
Correct answer : (1)
3.
The table shows the number of coins collected by 5 students. 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.
| Students | Number of coins |
| Brian | 18 |
| Charles | 10 |
| Catherine | 16 |
| Cindy | 20 |
| Jack | 16 |
| a. | Plot 1, 10 | |
| b. | Plot 3, 10 | ||
| c. | Plot 4, 30 | ||
| d. | Plot 2, 18 |
Solution:
The ascending order of the number of coins collected by each student is 10, 16, 16, 18, 20.In the table, least value is 10 and the greatest value is 20.
Middle quartile = median of the entire data = 16
=
Lower quartile = median of lower half of the data
[Add and simplify.]
=
Upper quartile = Median of upper half of the data
[Add and simplify.]
Plot (1) is the equivalent box-and-whisker plot for the data.
= Greatest value - Least value
Range of the box-and-whisker plot
= 20 - 10 = 10.
[Substitute and subtract.]
Correct answer : (1)
4.
The box-and-whisker plot shows the earnings (in dollars) of a daily wage earner. Find the range of his earnings.
| a. | $125 | |
| b. | $200 | ||
| c. | $150 | ||
| d. | $100 |
Solution:
From the box-and-whisker plot, least value = $75 and greatest value = $200Range = Greatest value - Least value
= $200 - $75 = $125
[Substitute and subtract.]
Range of the earnings = $125
Correct answer : (1)
5.
The box-and-whisker plot shows the weekly practice hours of two baseball teams. Which of the following statements are true?
| a. | Average median practice hours for Team B is greater than Team A. | ||
| b. | Average median practice hours are same for both the teams. | |
| c. | Upper quartile for Team A is less than the median of Team B | ||
| d. | Average median practice hours for Team A is greater than Team B. |
Solution:
From the plot average median practice hours are same for both the teams.Correct answer : (2)
6.
The box-and-whisker plot shows the average speed of two cars in reaching a destination. Which of the following statements is true?
| a. | Average median speed of Car B is greater than Car A. | |
| b. | Average median speed is same for both the Cars. | ||
| c. | Car B has lower average median speed than Car A. | ||
| d. | Lower quartile of the Car A is greater than the median of the Car B. |
Solution:
From the plot average median speed of Car B is greater than Car A.
Correct answer : (1)
7.
The box-and-whisker plot shows the heights of boys and girls in a school. Which of the following conclusions is true for the data?
| a. | Minimum height of the boys is equal to the minimum height of the girls. | ||
| b. | Minimum height of the girls is fairly close to the maximum height of the boys. | ||
| c. | Maximum height of the girls is fairly close to the maximum height of the boys. | |
| d. | 75% of the girls are taller than the shortest boy. |
Solution:
From the plot maximum height of the girls is fairly close to the maximum height of the boys.
Correct answer : (3)
8.
The box-and-whisker plot shows the weekly earnings($) of two different workers. Which of the following statements is true for the data?
| a. | Lower quartile of Worker B is equal to the median of Worker A. | ||
| b. | Median of Worker B is greater than median of Worker A. | ||
| c. | Range of Worker A is greater than the range of Worker B. | |
| d. | Median of the data is same for both the workers. |
Solution:
Range = Greatest value - Least ValueFrom the plot, range of Worker A is 250 - 100 = 150.
From the plot, range of Worker B is 200 - 75 = 125.
Range of Worker A is greater than the range of Worker B.
Correct answer : (3)
9.
Find the interquartile range from the given box-and-whisker plot.
| a. | 37.5 | ||
| b. | 12.5 | ||
| c. | 25 | |
| d. | 50 |
Solution:
Interquartile range is the difference between the upper quartile and the lower quartile.From the given box and whisker plot, the upper quartile is 37.5 and the lower quartile is 12.5.
= 37.5 - 12.5 = 25
Interquartile range = upper quartile - lower quartile
So, the interquartile range for the given box and whisker plot is 25.
Correct answer : (3)
10.
The box-and-whisker plot shows the earnings (in dollars) of a daily wage earner. Find the interquartile range.
| a. | 150 | ||
| b. | 200 | |
| c. | 100 | ||
| d. | 300 |
Solution:
The interquartile range is the difference between the upper quartile and the lower quartile.From the given box and whisker plot, the upper quartile is 300 and the lower quartile is 100.
= 300 - 100 = 200
Interquartile range = upper quartile - lower quartile
So, the interquartile range for the given box and whisker plot is 200.
Correct answer : (2)