1. Box-and-Whisker Plots
Making and Interpreting Box-and-Whisker Plots
Becky Afghani LBUSD Math Office

2. You will:
Construct and
Interpret
Box and Whisker Plots

3. What is a Box-and Whisker Plot?
Suppose you have a large set of data and want to know how it is distributed.
Think of a teacher’s class set of test scores.
A box-and-whisker plot displays the median, the quartiles, and the greatest and least values.

4. Why use a Box-and Whisker Plot?
The box-and-whisker plot is a visual way to show the data.
The median and quartiles can easily be read.
The shape of the box and the whiskers gives information about how the numbers are spread out.

5. Who uses Box-and Whisker Plots?
Scientists who perform experiments display their results using box-and-whisker plots.
Medical researchers display their findings using box-and-whisker plots.
Anyone who reads a scientific report needs to understand how a box-and-whisker works.

6. We will make a Box-and Whisker Plot
Here are all of the test scores from your class on the last math test. (Not really!) 87 75 83 94
100 74 68 98 99 85 72

7. You will need a five-number summary in order to construct the box-and-whisker plot.
Minimum
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum ?

8. Step 1: Write the data in order from least to greatest.87 75 83 94
100 74 68 98 99 85 72
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

9. Step 2: Find the minimum and maximum values of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
minimum
maximum
The minimum is 68.
The maximum is 100.
The 5 number Summary
Minimum
1st (lower) quartile
Median(2nd Q)
3rd (upper) quartile
Maximum

10. Tell your neighbor how to find the minimum and maximum.

11. Step 3: Find the median of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
7 in the upper half
7 in the lower half
1 in the middle
The 5 number Summary
Minimum 68
1st (lower) quartile
Median(2nd Q)
3rd (upper) quartile
Maximum
The median is 85.

12. Tell your neighbor how to find the median.

13. Step 4: Find the lower quartile (Q1) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
upper half
lower half
The middle number is not in the lower or upper half.

14. Step 4: Find the lower quartile (Q1) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
upper half
lower half
The lower quartile is 74.

15. Choral Response: What is the lower quartile?
The median of
the lower half

16. Step 5: Find the upper quartile (Q3) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
upper half
lower half
The middle number is not in the upper or upper half.

17. Step 5: Find the upper quartile (Q3) of the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100
upper half
lower half
The upper quartile is 99.

18. Choral Response: What is the upper quartile?
The median of
the upper half

19. Now that we have our five-number summary, we can construct the box-and-whisker plot.
Minimum
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum 68 74 85 99
100

20. Write in Your Notes: What are the five items in the five number summary?
I can think
of one...
I bet
he knows!

21. Step 6: Draw a number line that can show the data.
68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100 50 60 70 80 90
100

22. Step 7: Mark the minimum, maximum, median and both quartiles on the number line.
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum 68 74 85 99
100 50 60 70 80 90
100

23. Step 8: Draw a box between the lower and upper quartiles.
Minimum
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum 68 74 85 99
100 50 60 70 80 90
100

24. Step 9: Draw a vertical line through the median.
Minimum
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum 68 74 85 99
100 50 60 70 80 90
100

25. Step 10: Draw two “whiskers” from the quartiles to the minimum and maximum.
Lower quartile (Q1)
Median (Q2)
Upper quartile (Q3)
Maximum 68 74 85 99
100 50 60 70 80 90
100

26. Interpreting the box-and-whisker plot
25%
25%
25%
25% 50 60 70 80 90
100
Remember these are test scores.
25% of the test scores are in each whisker and each section of the box.

27. Find the false statement.74 85 99 68
100 50 60 70 80 90
100
A) One fourth of the test scores were between 85 and 99.
B) One half of the test scores were between 74 and 99.
C) One half of the test scores were between 85 and 100.
D) Three fourths of the test scores were between 68 and 85.

28. Make another box-and-whisker plot from this data:
Age at First Inauguration of
American Presidents from 1900 to 1999 4 5 6
42 is 42 years

29. Minimum and Maximum
Age at First Inauguration of
American Presidents from 1900 to 1999 4 5 6
42 is 42 years
42 is the minimum
69 is the maximum

30. 54.5 is the median Median What is halfway between 54 and 55? How many
data items
are there?
What is
half of 18?
Median
Age at First Inauguration of
American Presidents from 1900 to 1999 4 5 6
42 is 42 years ?
9th item
10th item
54.5 is the median
18 items

31. Lower Quartile 51 is the lower quartile How many items are
in the lower
half?
9 items
Which item
is in the
middle?
The 5th item
Lower Quartile
Age at First Inauguration of
American Presidents from 1900 to 1999 4 5 6
42 is 42 years
54.5
51 is the lower quartile

32. Upper Quartile 60 is the upper quartile How many items are
in the upper
half?
Upper Quartile
Age at First Inauguration of
American Presidents from 1900 to 1999 4 5 6
42 is 42 years
The 5th item
9 items
Which item
is in the
middle?
54.5
60 is the upper quartile

33. The Box-and-Whisker Plot
Age at First Inauguration of
American Presidents from 1900 to 1999 4 5 6
42 is 42 years
54.5 40 50 60 70

34. Find the false statement.40 50 60 70
A) The oldest president at his inauguration was 69.
B) One fourth of the presidents were 60 or over when inaugurated.
C) One half of the presidents were inaugurated between ages 50 and 60.
D) The youngest president to be inaugurated in the 1900s was 42.

35. Multiple Box-and-Whisker Plots Can Be Used to Compare Data
Describe the variability between the data sets and compare the two 5 number summaries 10 20 30 40 50 60 70 80 90
100
Average Monthly High Temperatures in Anchorage, Alaska 10 20 30 40 50 60 70 80 90
100
Average Monthly High Temperatures in Long Beach, California

36. Find the false statement.
Average Monthly High Temperatures in Anchorage, Alaska 10 20 30 40 50 60 70 80 90
100 10 20 30 40 50 60 70 80 90
100
Average Monthly High Temperatures in Long Beach, California
A) The range of average monthly high temperatures is broader in Anchorage than in Long Beach.
B) The average monthly high temperatures in Long Beach are warmer than Anchorage.
C) Half of the average monthly highs in Long Beach are between 27 and 59 degrees.

37. In your notes...
1. List the five items required for a box-and-whisker plot.
2. Write a short description for each.