Do Now1. What percent of students chose math as their favorite class?
Hwk: 62, test on Wednesday ch7 sec1-5
Course 2
7-5 Box-and-Whisker Plots
Favorite Class
Class Frequency
LA 12
Math 8
Science 9
Social Studies 5
other 6
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).
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
Course 2
7-5 Box-and-Whisker Plots
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
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.
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!
Use the data to make a box-and-whisker plot.
Additional Example 1: Making a Box-and-Whisker Plot
Course 2
7-5 Box-and-Whisker Plots
73 67 75 81 67 75 85 69
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 67 69 73 75 75 81 85
Find the median.67 67 69 73 75 75 81 85
2
+
=74
Additional Example 1 Continued
Course 2
7-5 Box-and-Whisker Plots
67 67 69 73 75 75 81 85
lower quartile = 67 + 692
= 68
upper quartile = 75 + 81
2= 78
Step 1 Continued
Additional Example 1 Continued
Course 2
7-5 Box-and-Whisker Plots
Step 2: Draw a number line.
64 66 68 70 72 74 76 78 80 82 84 86
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.
Check It Out: Example 1
Course 2
7-5 Box-and-Whisker Plots
Use the data to make a box-and-whisker plot.
42 22 31 27 24 38 35
22 24 27 31 35 38 42
22 24 27 31 35 38 42
The least value.
The greatest value.
The median.
The upper and lower quartiles.22 24 27 31 35 38 42
Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upper quartiles.
Check It Out: Example 1 Continued
Course 2
7-5 Box-and-Whisker Plots
Step 2: Draw a number line.
20 22 24 26 28 30 32 34 36 38 40 42
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.
Course 3
9-4 Variability
Litter Size 2 3 4 5 6
Number of Litters
1 6 8 11 1
The table below summarizes a veterinarian’s records for kitten litters born in a given year.
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.
Find the first and third quartiles for the data set.
Additional Example 1A: Finding Measures of Variability
Course 3
9-4 Variability
15, 83, 75, 12, 19, 74, 21
12 15 19 21 74 75 83 Order the values.
first quartile: 15
third quartile: 75
Find the first and third quartiles for the data set.
Additional Example 1B: Finding Measures of Variability
Course 3
9-4 Variability
75, 61, 88, 79, 79, 99, 63, 77
61 63 75 77 79 79 88 99
first quartile: = 6963 + 752
third quartile: = 83.579 + 882
Order the values.
Find the first and third quartiles for the data set.
Check It Out: Example 1A
Course 3
9-4 Variability
25, 38, 66, 19, 91, 47, 13
13 19 25 38 47 66 91 Order the values.
first quartile: 19
third quartile: 66
Course 3
9-4 Variability
45, 31, 59, 49, 49, 69, 33, 47
31 33 45 47 49 49 59 69 Order the values.
Find the first and third quartiles for the data set.
Check It Out: Example 1B
first quartile: = 3933 + 452
third quartile: = 5449 + 592
Course 3
9-4 Variability
1 2 3 4 5 6 7 8 9
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.
First quartile Third quartileMedian
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
Course 3
9-4 Variability
Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value.
13 15 17 19 19 21 21 25
smallest value: 13 largest value: 25
first quartile: = 16 15 + 172 third quartile: = 2121 + 21
2
median: = 1919 + 192
Use the given data to make a box-and-whisker plot.
Course 3
9-4 Variability
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.
smallest value 13
13 15 17 19 19 21 21 25first quartile 16
median 19
third quartile 21
largest value 25
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Course 3
9-4 Variability
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
Use the box-and-whisker plots below to answer each question.
Additional Example 2A: Comparing Box-and-Whisker Plot
Course 2
7-5 Box-and-Whisker Plots
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.
64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.)
Basketball Players
Baseball Players
Use the box-and-whisker plots below to answer each question.
Additional Example 2B: Comparing Box-and-Whisker Plot
Course 2
7-5 Box-and-Whisker Plots
Which players have a greater interquartile range?
The basketball players have a longer box, so they have a greater interquartile range.
64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.)
Basketball Players
Baseball Players
Use the box-and-whisker plots below to answer each question.
Additional Example 2C: Comparing Box-and-Whisker Plot
Course 2
7-5 Box-and-Whisker Plots
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.
64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.)
Basketball Players
Baseball Players
Use the box-and-whisker plots below to answer each question.
Check It Out: Example 2A
Course 2
7-5 Box-and-Whisker Plots
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.
20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store
Maroon’s Shoe Store
Sage’s Shoe Store
Use the box-and-whisker plots below to answer each question.
Check It Out: Example 2B
Course 2
7-5 Box-and-Whisker Plots
Which shoe store has a greater interquartile range?
Maroon’s shoe store has a longer box, so it has a greater interquartile range.
20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store
Maroon’s Shoe Store
Sage’s Shoe Store
Use the box-and-whisker plots below to answer each question.
Check It Out: Example 2C
Course 2
7-5 Box-and-Whisker Plots
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.
20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store
Maroon’s Shoe Store
Sage’s Shoe Store
Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots
Course 3
9-4 Variability
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.
Note: 57 is the first quartile and the median.
Additional Example 3 Continued
Course 3
9-4 Variability
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.
Note: 57 is the first quartile and the median.
Additional Example 3 Continued
Course 3
9-4 Variability
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.
Note: 57 is the first quartile and the median.
Check It Out: Example 3
Course 3
9-4 Variability
Final 1 2 3 4 T
Oakland 3 0 6 12 21
Tampa Bay 3 17 14 14 48
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.
Oakland
0 3 6 9 12 15 18
Tampa Bay
0 3 6 9 12 15 18
Course 3
9-4 Variability
Compare the medians and ranges.
Check It Out: Example 3A
The median for Tampa Bay is significantly greater, however the range for Tampa Bay is slightly greater.
Oakland
0 3 6 9 12 15 18
Tampa Bay
0 3 6 9 12 15 18
Course 3
9-4 Variability
Compare the differences between the third quartile and first quartile for each.
Check It Out: Example 3B
The difference between the third quartile and first quartile is the length of the box, which is slightly greater for Oakland.
Oakland
0 3 6 9 12 15 18
Tampa Bay
0 3 6 9 12 15 18
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
Course 2
7-5 Box-and-Whisker Plots
18 20 22 24 26 28 30 32 34 36 38 40
TOTD
4. Compare the box-and-whisker plots below. Which has the greater interquartile range?
They are the same.
Course 2
7-5 Box-and-Whisker Plots
18 20 22 24 26 28 30 32 34 36 38 40
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 = 2.5; Q3 = 12
Q1 = 47; Q3 = 53
Insert Lesson Title Here
Course 3
9-4 Variability
Lesson Quiz: Part II
Use the following data for problems 3 and 4.
91, 87, 98, 93, 89, 78, 94
3. Make a box-and-whisker plot
4. What is the mean?
Insert Lesson Title Here
Course 3
9-4 Variability
90
78 87 91 94 98