1. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Favorite Class
Class
Frequency LA 12
Math 8
Science 9
Social Studies 5
other 6
Do Now
What percent
of students chose
math as their
favorite class?
Hwk: 62, test on Wednesday
ch7 sec1-5

2. 1d: Analyze data with respect to measures of variations
EQ: How do I display(show) and analyze(figure out) data in box-and-whisker plots?
1d: Analyze data with respect to
measures of variations
(range, quartiles, interquartile range).

3. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
box-and-whisker plot – graph that displays the highest and lowest quarters of data as whiskers and the middle two quarters of the data as a box, and the median

4. lower quartile – the median of the lower half of a set of data
upper quartile – the median of the upper half of a set of data
interquartile range – difference between upper and lower quartiles in a box and whisker plot

5. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
A box-and-whisker plot uses a number line to show the distribution of a set of data.
To make a box-and-whisker plot, first divide the data into four equal parts using quartiles. The median, or middle quartile, 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.

6. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
To find the median of a data set with an even number of values, find the mean of the two middle values.
Caution!

7. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Additional Example 1: Making a Box-and-Whisker Plot
Use the data to make a box-and-whisker plot.
Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upper quartiles.
The least value.
The greatest value. 67 69 73 75 81 85 67 69 73 75 81 85 +
Find the median. 2
=74

8. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Additional Example 1 Continued
Step 1 Continued 67 69 73 75 81 85
lower quartile =
= 68 2
upper quartile =
= 78 2

9. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Additional Example 1 Continued
Step 2: Draw a number line.
Above the number line, plot points for each value in Step 1.
Step 3: Draw a box from the lower to the upper quartile.
Inside the box, draw a vertical line through the median.
Then draw the “whiskers” from the box to the least and greatest values.

10. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Check It Out: Example 1
Use the data to make a box-and-whisker plot.
Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upper quartiles.
The least value.
The greatest value. 22 24 27 31 35 38 42 22 24 27 31 35 38 42
The median.
The upper and lower quartiles. 22 24 27 31 35 38 42

11. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Check It Out: Example 1 Continued
Step 2: Draw a number line.
Above the number line, plot a point for each value in Step 1.
Step 3: Draw a box from the lower to the upper quartile.
Inside the box, draw a vertical line through the median.
Then draw the “whiskers” from the box to the least and greatest values.

12. 9-4 Variability Litter Size 2 3 4 5 6 Number of Litters 1 8 11
Course 3
9-4
Variability
The table below summarizes a veterinarian’s records for kitten litters born in a given year.
Litter Size 2 3 4 5 6
Number of Litters 1 8 11
While central tendency describes the middle of a data set, variability describes how spread out the data is. Quartiles divide a data set into four equal parts. The third quartile minus the first quartile is the range for the middle half of the data which is known as Interquartile Range.

13. Additional Example 1A: Finding Measures of Variability
Course 3
9-4
Variability
Additional Example 1A: Finding Measures of Variability
Find the first and third quartiles for the data set.
15, 83, 75, 12, 19, 74, 21
Order the values.
first quartile: 15
third quartile: 75

14. Additional Example 1B: Finding Measures of Variability
Course 3
9-4
Variability
Additional Example 1B: Finding Measures of Variability
Find the first and third quartiles for the data set.
75, 61, 88, 79, 79, 99, 63, 77
Order the values.
first quartile: = 69 2
third quartile: = 83.5 2

15. 9-4 Variability Check It Out: Example 1A
Course 3
9-4
Variability
Check It Out: Example 1A
Find the first and third quartiles for the data set.
25, 38, 66, 19, 91, 47, 13
Order the values.
first quartile: 19
third quartile: 66

16. 9-4 Variability Check It Out: Example 1B
Course 3
9-4
Variability
Check It Out: Example 1B
Find the first and third quartiles for the data set.
45, 31, 59, 49, 49, 69, 33, 47
Order the values.
first quartile: = 39 2
third quartile: = 54 2

17. Course 3
9-4
Variability
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 lower fourth and upper fourth quarters are represented by “whiskers” that extend to the smallest and largest values.
Median
First quartile
Third quartile

18. Additional Example 2: Making a Box-and-Whisker Plot
Course 3
9-4
Variability
Additional Example 2: Making a Box-and-Whisker Plot
Use the given data to make a box-and-whisker plot:
21, 25, 15, 13, 17, 19, 19, 21
Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value.
smallest value: 13
largest value: 25
first quartile: = 16 2
third quartile: = 21 2
median: = 19 2

19. Additional Example 2 Continued
Course 3
9-4
Variability
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above each value from Step 1.
smallest value 13
first quartile 16
median 19
third quartile 21
largest value 25

20. Use the given data to make a box-and-whisker plot.
Course 3
9-4
Variability
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 3. Draw the box and whiskers.

30. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Additional Example 2A: Comparing Box-and-Whisker Plot
Use the box-and-whisker plots below to answer each question.
Basketball Players
Baseball Players
t Heights of Basketball and Baseball Players (in.)
Which set of heights of players has a greater median?
The median height of basketball players, about 74 inches, is greater than the median height of baseball players, about 70 inches.

31. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Additional Example 2B: Comparing Box-and-Whisker Plot
Use the box-and-whisker plots below to answer each question.
Basketball Players
Baseball Players
t Heights of Basketball and Baseball Players (in.)
Which players have a greater interquartile range?
The basketball players have a longer box, so they have a greater interquartile range.

32. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Additional Example 2C: Comparing Box-and-Whisker Plot
Use the box-and-whisker plots below to answer each question.
Basketball Players
Baseball Players
t Heights of Basketball and Baseball Players (in.)
Which group of players has more predictability in their height?
The range and interquartile range are smaller for the baseball players, so the heights for the baseball players are more predictable.

33. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Check It Out: Example 2A
Use the box-and-whisker plots below to answer each question.
Maroon’s Shoe Store
Sage’s Shoe Store
t Number of Shoes Sold in One Week at Each Store
Which shoe store has a greater median?
The median number of shoes sold in one week at Sage’s Shoe Store, about 32, is greater than the median number of shoes sold in one week at Maroon’s Shoe Store, about 28.

34. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Check It Out: Example 2B
Use the box-and-whisker plots below to answer each question.
Maroon’s Shoe Store
Sage’s Shoe Store
t Number of Shoes Sold in One Week at Each Store
Which shoe store has a greater interquartile range?
Maroon’s shoe store has a longer box, so it has a greater interquartile range.

35. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
Check It Out: Example 2C
Use the box-and-whisker plots below to answer each question.
Maroon’s Shoe Store
Sage’s Shoe Store
t Number of Shoes Sold in One Week at Each Store
Which shoe store appears to be more predictable in the number of shoes sold per week?
The range and interquartile range are smaller for Sage’s Shoe Store, so the number of shoes sold per week is more predictable at. Sage’s Shoe Store.

36. Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots
Course 3
9-4
Variability
Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots
Note: 57 is the first quartile and the median.
These box-and-whisker plots compare the ages of the first ten U.S. presidents with the ages of the last ten presidents (through George W. Bush) when they took office.

37. Additional Example 3 Continued
Course 3
9-4
Variability
Additional Example 3 Continued
Note: 57 is the first quartile and the median.
A. Compare the medians and ranges.
The median for the first ten presidents is slightly greater. The range for the last ten presidents is greater.

38. Additional Example 3 Continued
Course 3
9-4
Variability
Additional Example 3 Continued
Note: 57 is the first quartile and the median.
B. Compare the differences between the third quartile and first quartile for each.
The difference between the third quartile and first quartile is the length of the box, which is greater for the last ten presidents.

39. 9-4 Variability Check It Out: Example 3 Oakland
Course 3
9-4
Variability
Check It Out: Example 3
Final 1 2 3 4 T
Oakland 6 12 21
Tampa Bay 17 14 48
Oakland
Tampa Bay
These box-and-whisker plots compare the scores per quarter at Super Bowl XXXVII. The data in the T column is left out because it is a total of all the quarters.

40. 9-4 Variability Check It Out: Example 3A
Course 3
9-4
Variability
Check It Out: Example 3A
Compare the medians and ranges.
Oakland
Tampa Bay
The median for Tampa Bay is significantly greater, however the range for Tampa Bay is slightly greater.

41. 9-4 Variability Check It Out: Example 3B
Course 3
9-4
Variability
Check It Out: Example 3B
Compare the differences between the third quartile and first quartile for each.
Oakland
Tampa Bay
The difference between the third quartile and first quartile is the length of the box, which is slightly greater for Oakland.

42. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
TOTD
Use the data for Questions 1-3.
24, 20, 18, 25, 22, 32, 30, 29, 35, 30, 28, 24, 38
1. Create a box-and-whisker plot for the data.
2. What is the range?
3. What is the 3rd quartile? 20 31

43. Box-and-Whisker Plots
Course 2
7-5
Box-and-Whisker Plots
TOTD
4. Compare the box-and-whisker plots below. Which has the greater interquartile range?
They are the same.

44. Insert Lesson Title Here
Course 3
9-4
Variability
Insert Lesson Title Here
Lesson Quiz: Part I
Find the first and third quartile for each data set.
1. 48, 52, 68, 32, 53, 47, 51
2. 3, 18, 11, 2, 7, 5, 9, 6, 13, 1, 17, 8, 0
Q1 = 47; Q3 = 53
Q1 = 2.5; Q3 = 12

45. Insert Lesson Title Here
Course 3
9-4
Variability
Insert Lesson Title Here
Lesson Quiz: Part II
Use the following data for problems 3 and , 87, 98, 93, 89, 78, 94
3. Make a box-and-whisker plot
4. What is the mean? 90