Ms. Goodwin – Math 10X – Box-and-Whisker Plots
Constructing a Box-and-Whisker Plot:
The data: Math test scores 80, 75, 90, 95, 65, 65, 80, 85, 70, 100
Write the data in numerical
order and find the first quartile,
the median, the third quartile,
the smallest value and the
largest value.
median = 80
first quartile = 70
third quartile = 90
smallest value = 65
largest value = 100
Place a circle beneath each of
these values on a number line.
Draw a box with ends through
the points for the first and third
quartiles. Then draw a vertical
line through the box at the
median point. Now, draw the
whiskers (or lines) from each
end of the box to the smallest
and largest values.
Notes:


Box-and-whisker plots are helpful in interpreting the distribution of data.
We know that the median (also called the second quartile) of a set of
data separates the data into two equal parts. Data can be further separated
into quartiles.
 The first quartile is the median of the lower part of the data. It is also
called the lower quartile.
 The third quartile is the median of the upper part of the data. It is also
called the upper quartile.
Sample Box-and-Whisker Plot:
Exercises:
1. Draw a box-and-whisker plot for the following data set:
4.3,
5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.7, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4
The first step is to order the set. I have already done this for you to save time:
3.9, 4.1, 4.2, 4.3, 4.3, 4.4, 4.4, 4.4, 4.4, 4.5, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, 5.1
Next, you must find the five values required to create the box-and-whisker plot:
Lower Extreme
Lower Quartile
Median
Upper Quartile
Upper Extreme
Now, plot these five values above the number line below and draw a box from the
lower quartile to the upper quartile with whiskers drawn from the edges of this box
towards the lower and upper extremes.
2. Draw the box-and-whisker plot for the following data set:
77, 79, 80, 86, 87, 87, 94, 99
Lower Extreme
Lower Quartile
Median
Upper Quartile
Upper Extreme
3. Draw the box-and-whisker plot for the following data set:
79, 53, 82, 91, 87, 98, 80, 93
Lower Extreme
Lower Quartile
Median
Upper Quartile
Upper Extreme
4. Subjects in a psychological study were timed while completing a certain task. Complete
a box-and-whisker plot for the following list of times:
7.6, 8.1, 9.2, 6.8, 5.9, 6.2, 6.1, 5.8, 7.3, 8.1, 8.7, 7.4, 7.8, 8.2
Lower Extreme
Lower Quartile
Median
Upper Quartile
Upper Extreme
5.
5. The following data presents the number of cases of tomato soup sold per week
at a local supermarket over a period of 28 weeks:
Week Sold Week Sold Week Sold
1
81
11
86
21
91
2
61
12 133
22
99
3
77
13
91
23
89
4
71
14 111
24
96
5
69
15
86
25 108
6
81
16
84
26
86
7
66
17 131
27
84
8 111
18
28
76
9
56
19 118
10
81
20
71
88
Construct a box and whisker plot for this data.
Math 10X - Ms. Goodwin - Interpreting Box-and-Whisker Plots
1. Comparing the Quality Ratings for Natural/Regular Peanut Butters:
a)
b)
c)
d)
For the regular brand of peanut butter, what percentage of the data is below the quality rating of 40?
For the regular brand of peanut butter, what percentage of the data is above the quality rating of 53?
For the natural brand of peanut butter, what percentage of the data is below the quality rating of 56?
What is the median quality rating for the natural brand of peanut butter?
2. Comparing heights of plants:
a)
b)
c)
d)
e)
Which sample of plants has the lowest range of heights?
A plant from which sample is most likely to be near 20 cm tall? Explain your reasoning.
What percentage of each sample of plants is above 20 cm tall?
Between which heights for the plants in sample A will you find the middle 50% of the plants?
Between which heights for the plants in sample B will you find the middle 50% of the plants?
3. Comparing deaths due to lung cancer:
a) What age group is most likely to die of lung cancer? Explain your choice.
b) What age group is least likely to die of lung cancer? Explain your choice.
How's the Weather?
You and your family have decided to seek your fortunes in a new city in the United States. You have
collected some weather data for several cities that seem interesting and are going to compare the
temperatures with a box and whiskers. One of the cities you are considering is San Francisco. The table
below shows the average monthly temperatures in degrees Celsius for both Louisville and San Francisco
(www.worldclimate.com).
Month
Louisville
San Francisco
January
-0.1
9.2
February
2.0
11.2
March
7.9
11.8
April
13.5
13.1
May
18.5
14.5
June
22.8
16.3
July
25.1
17.0
August
24.3
17.6
September
20.8
18.0
October
14.2
16.1
November
8.3
12.6
December
2.7
9.6
Make a box plot of the temperature data for Louisville in the space provided below.
Lower Extreme
Lower Quartile
Median
Upper Quartile
Upper Extreme
1. What is the median temperature in Louisville?
2. What does the range of data between the upper and lower quartile tell us about Louisville's temperatures?
3. Do the monthly temperatures seem close together or varied? Explain your reasoning based on the box
and whiskers plot.
Make a second box plot of the temperatures for San Francisco.
Lower Extreme
Lower Quartile
Median
Upper Quartile
Upper Extreme
1. What is the median temperature in San Francisco?
2. What does the range of data between the upper and lower quartile tell us about Louisville's temperatures?
3. Do the monthly temperatures seem close together or varied? Explain your reasoning based on the box
and whiskers plot.
Consider the box-and-whiskers plots for both cities.
1. Compare the median temperatures in San Francisco and Louisville. Based on the median temperatures,
could you conclude that temperatures in the two cities are similar? Explain your reasoning.
2. What can you conclude about temperatures in the two cities based on the box and whiskers plots?
3. If you like a wide change in temperatures throughout the year, which city would you want to move to?
Explain.