#### Solved Examples and Worksheet for Interpreting Box Plots and Finding Interquartile Range

Q1What is the outlier in the box and whisker plot? A. 92
B. 84
C. 90
D. No outlier

Step: 1
In a box and whisker plot outlier is the data value that should be less than the [lower quartile - (1.5 x IQR)] or greater than the [upper quartile + (1.5 x IQR)].
Step: 2
IQR = upper quartile - lower quartile
= 100 - 90 = 10
[upper quartile = 100 and lower quartile = 90.]
Step: 3
Lower quartile - (1.5 x IQR) = 90 - (1.5 x 10) = 75
[Substitute and subtract.]
Step: 4
Upper quartile + (1.5 x IQR) = 100 + (1.5 x 10) = 115
[Substitute and simplify.]
Step: 5
In the box and whisker plot all the values are between 82 and 106. So, there is no value less than 75 or greater than 115.
Step: 6
So, in the data there is no outlier.
Correct Answer is :   No outlier
Q2The 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
Q3John traveled from place A to B at different speeds. The box-and-whisker plot shows the speeds. Find the median speed of the car. A. 80 miles/ hour
B. 50 miles/ hour
C. 10 miles/ hour
D. 100 miles/ hour

Step: 1
Median of a given data is equal to the middle quartile value in its equivalent box-and-whisker plot.
Step: 2
From the box-and-whisker plot, the middle quartile value = 80.
Step: 3
So, the median speed of the car = 80 miles/ hour.
Correct Answer is :   80 miles/ hour
Q4What is the difference between the middle quartile and the least value in the box-and-whisker plot? A. 40
B. 50
C. 10
D. 80

Step: 1
From the box-and-whisker plot, least value = 10 and middle quartile = 50.
Step: 2
The difference between the middle quartile and the least value = middle quartile - least value
= 50 - 10
= 40

Q5Find the outlier for the box and whisker plot. A. 6
B. 7
C. 16
D. No outlier

Step: 1
From the box and whisker plot, lower quartile is 7 and upper quartile is 11.
[Lower quartile is the median of the lower half and upper quartile is the median of the upper half of data set.]
Step: 2
Outlier for the box and whisker plot is the value less than (lower quartile- 1.5 x IQR) or the value greater than (upper Quartile +1.5 x IQR).
[IQR = inter quartile range = upper quartile - lower quartile.]
Step: 3
IQR for the box and whisker plot = 11 - 7 = 4
[Subtract lower quartile value from upper quartile value.]
Step: 4
(Lower Quartile - 1.5 x IQR) = 7 - 1.5 x 4 = 7 - 6 = 1

Step: 5
Upper Quartile + 1.5 x IQR = 11 + 1.5 x 4 = 11 + 6 = 17

Step: 6
For being the outlier, the data value must be less than 1 or greater than 17.
Step: 7
There is no such value in the plot as the least value of the plot is 5 and the highest value is 16.
Step: 8
So, there is no outlier for the box and whisker plot.
Correct Answer is :   No outlier
Q6The scores of students on a math test are 30, 8, 10, 12, 14, 17, 21, 23, 28, 17 and 13. What is the middle quartile of the data?
A. 17
B. 14
C. 8
D. 30

Step: 1
The ascending order of the above data set is 8, 10, 12, 13, 14, 17, 17, 21, 23, 28, 30.
Step: 2
The middle quartile = Median of the entire data set = 17

Q7The box-and-whisker plot shows the number of books sold per day in a month. Find out the lower quartile of the box-and-whisker plot. A. 48
B. 46
C. 53
D. 52

Step: 1
The lower quartile is the median of the data values from the least value to the middle quartile.
Step: 2
The box in a box-and-whisker plot always starts from the lower quartile value.
Step: 3
The lower quartile of the box-and-whisker plot = 48.
Q8The box-and-whisker plot shows the distance covered (in kilometers) during a benefit walk. What is the range of the data? A. 2.1
B. 1.5
C. 4.5
D. 2.5

Step: 1
From the box-and-whisker plot, the greatest value is 18.2 and the least value is 16.1
Step: 2
Range = Greatest value - Least value
Step: 3
Range of the given data = 18.2 - 16.1 = 2.1
[Subtract.]
Q9The number of games won by a famous basketball team each year from the year 1991 to the year 2000 are 25, 30, 25, 50, 40, 75, 40, 50, 35, and 40. Find the interquartile range for the given data.
A. 20.5
B. 22.5
C. 40
D. 20

Step: 1
The interquartile range is the difference between the upper quartile and the lower quartile.
Step: 2
Arrange the given data in ascending order
25, 25, 30, 35, 40, 40, 40, 50, 50, 75
Step: 3
Lower quartile = 30
Upper quartile = 50
Step: 4
Interquartile range = upper quartile - lower quartile
= 50 - 30 = 20

Step: 5
So, the interquartile range for the given data is 20.
Q10Find the interquartile range of these 12 scores: 10, 11, 12, 15, 15, 17, 18, 19, 19, 21, 21, 22.

A. 13.5
B. 6.5
C. 9
D. 20

Step: 1
Interquartile range is the difference between the upper quartile and the lower quartile.
Step: 2 Step: 3
Interquartile range = upper quartile - lower quartile
= 21 - 13.5 = 6.5

Step: 4
So, the interquartile range of the scores given is 6.5.
Q11The owner of a super market recorded the number of customers who came into his store each hour for one day. The results were 5, 8, 10, 9, 9, 11, 10, 13, 12, 3, and 2. Find the interquartile range.
A. 6
B. 15
C. 10
D. 9

Step: 1
The interquartile range is the difference between the upper quartile and the lower quartile.
Step: 2
Arrange the given data in ascending order
2,3,5,8,9,9,10,10,11,12,13
Step: 3 Step: 4
Lower quartile = 5
Upper quartile = 11
Step: 5
Interquartile range = upper quartile - lower quartile
= 11 - 5 = 6

Step: 6
So, the interquartile range for the given data is 6.
Q12Find the interquartile range from the given box-and-whisker plot. A. 4
B. 3.5
C. 5
D. 7.5

Step: 1
Interquartile range is the difference between upper quartile and lower quartile of a data set.
Step: 2
Label lower and upper quartiles in the given figure as shown below. Step: 3
Upper quartile in the above figure = 12.5.
Lower quartile in the above figure = 17.5.
Step: 4
Interquartile range = upper quartile - lower quartile
Step: 5
= 17.5 - 12.5
[From step 3.]
Step: 6
= 5
[Subtract.]
Step: 7
Therefore, interquartile range in the given figure is 5.
Q13Micky wants to find the number of hours that students in his school spend in playing games. Identify the best sampling method for him to use.