1. SDAP1.1 Know various forms of
display for data sets, including a stem-
and-leaf plot or box-and-whisker plot;
use the forms to display a single set of
data or to compare two sets of data.
SDAP1.3 Understand the
meaning of, and be able to compute,
the minimum, the lower quartile, the
median, the upper quartile, and the
maximum of a data set.
California
Standards
3. APK
Teacher I do
1. Order the test scores from least to
greatest: 89, 93, 79, 87, 91, 88, 92.
2. Find the median of the test scores.
79, 87, 88, 89, 91, 92, 93
89
Find the median of the following test scores?
65, 75, 92, 90, 74, 86, 98
Students complete:
We will need to know how to find the median in order
to make box and whisker plots.
5. 78 85 88 88 89 90 92
A box-and-whisker plot shows the distribution of data.
The middle half of the data is represented by a “box” with
a vertical line at the median.
The box extends to the upper and lower quartiles.
The upper quartile is the median of the upper half of the
data. The lower quartile is the median of the lower half
of the data.
Lower quartile Upper quartile
Median
Data set: 85,92,78,88,90,88,89
What is a box-and-whisker plot?
What are the upper and lower quartiles?
6. 78 85 88 88 89 90 92
The lower fourth and upper fourth quarters are
represented by “whiskers” that extend to the minimum
(least) and maximum (greatest) values.
Lower quartile Upper quartile
Median
Data set: 85,92,78,88,90,88,89
What are minimum and maximum values?
7. Litter Size 2 3 4 5 6
Number of
Litters
1 6 8 11 1
The table below summarizes a cat breeder’s
records for kitten litters born in a given year. You
can divide the data into four equal part using
quartiles.
8. Kitten Data
2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6
Lower half Upper half
Lower quartile: 3
median of lower half
Upper quartile: 5
median of upper half
Median: 4
You know that the median of a data set divides the
data into a lower half and an upper half. The median
of the lower half is the lower quartile, and the
median of the upper half is the upper quartile.
9. Kitten Data
2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6
Lower half Upper half
Lower quartile: 3
median of lower half
Upper quartile: 5
median of upper half
Median: 4
You know that the median of a data set divides the
data into a lower half and an upper half. The median
of the lower half is the lower quartile, and the
median of the upper half is the upper quartile.
10. 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6
Lower half Upper half
A
B c
D
E
F
How do you know?
What letter is the _____?
11. Importance
Why do we need to know how to display and analyze
data in box-and-whisker plots ?
*It helps you to interpret and represent data.
*It gives a visual representation of data.
Tell your partner which reason is most important to
you. You can use one of mine or one of your own.
p/s - volunteers
12. Find the lower and upper quartiles for the data
set.
A. 15, 83, 75, 12, 19, 74, 21
12 15 19 21 74 75 83
Order the values.
lower quartile: 15
upper quartile: 75
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
I do
How did I find the lower and upper quartiles?
13. Find the lower and upper quartiles for the data
set.
B. 75, 61, 88, 79, 79, 99, 63, 77
61 63 75 77 79 79 88 99
lower quartile: = 69
63 + 75
2
upper quartile: = 83.5
79 + 88
2
Order the values.
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
We do
14. Find the lower and upper quartiles for the data
set.
A. 25, 38, 66, 19, 91, 47, 13
13 19 25 38 47 66 91 Order the values.
lower quartile: 19
upper quartile: 66
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
We do
15. B. 45, 31, 59, 49, 49, 69, 33, 47
31 33 45 47 49 49 59 69 Order the values.
Find the lower and upper quartiles for the data
set.
lower quartile: = 39
33 + 45
2
upper quartile: = 54
49 + 59
2
1. Order the data from least to greatest.
2. Find the median.
3. Find the median of the lower half – lower quartile
4. Find the median of the upper half – upper quartile
You do
16. Use the given data to make a box-and-whisker plot.
21, 25, 15, 13, 17, 19, 19, 21
Additional Example 2: Making a Box-and-Whisker Plot
Step 1. Order the data from least to greatest. Then
find the minimum, lower quartile, median, upper
quartile, and maximum.
13 15 17 19 19 21 21 25
minimum: 13 maximum: 25
lower quartile: = 16
15 + 17
2
upper quartile: = 21
21 + 21
2
median: = 19
19 + 19
2
I do:
17. Use the given data to make a box-and-whisker plot.
12 14 16 18 20 22 24 26 28
Step 2. Draw a number line and plot a point above
each value from Step 1.
13 15 17 19 19 21 21 25
Additional Example 2 Continued
I do (cont.)
18. Use the given data to make a box-and-whisker plot.
12 14 16 18 20 22 24 26 28
Step 3. Draw the box and whiskers.
13 15 17 19 19 21 21 25
Additional Example 2 Continued
I do (cont.)
19. 23 24 26 29 31 31 33 35
Use the given data to make a box-and-whisker plot.
31, 23, 33, 35, 26, 24, 31, 29
Check It Out! Example 2
Step 1. Order the data from least to greatest. Then
find the minimum, lower quartile, median, upper
quartile, and maximum.
minimum: 23 maximum: 35
lower quartile: = 25
24 + 26
2
upper quartile: = 32
31 + 33
2
median: = 30
29 + 31
2
We do
20. Use the given data to make a box-and-whisker plot.
22 24 26 28 30 32 34 36 38
Step 2. Draw a number line and plot a point above
each value.
23 24 26 29 31 31 33 35
Check It Out! Example 2 Continued
We do (cont.)
21. Step 2. Draw a number line and plot a point above
each value.
Use the given data to make a box-and-whisker plot.
22 24 26 28 30 32 34 36 38
Step 3. Draw the box and whiskers.
23 24 26 29 31 31 33 35
Check It Out! Example 2 Continued
We do (cont.)
22. Step 1. Order the data from least to greatest. Then find
the minimum, lower quartile, median, upper quartile, and
maximum.
Step 2. Draw a number line and plot a point above each
value.
Step 3. Draw the box and whiskers.
Additional Guided Practice:
With partners:
Page 544 #1
You do:
Page 544 #2
23. Closure
Find the lower and upper quartiles for each
data set.
1. 48, 52, 68, 32, 53, 47, 51
lower = 47; upper = 53
What uses upper and lower quartiles, the median, the
maximum, and the minimum to show a set of data?
24. Closure (cont.)
Use the following data for problems 3 and 4.
91, 87, 98, 93, 89, 78, 94
3. Make a box-and-whisker plot.
78 87 91 94 98
What did you learn today about box-and-whisker plots?
