do now 1.what percent of students chose math as their favorite class? hwk: 62, test on wednesday ch7...

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


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


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


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


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


67 67 69 73 75 75 81 85

lower quartile = 67 + 692

= 68

upper quartile = 75 + 81

2= 78

Step 1 Continued


Course 2


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


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


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


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.


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.


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


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


Use the box-and-whisker plots below to answer each question.

Additional Example 2A: Comparing Box-and-Whisker Plot

Course 2


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


Additional Example 2B: Comparing Box-and-Whisker Plot

Course 2


Which players have a greater interquartile range?

The basketball players have a longer box, so they have a greater interquartile range.


Basketball Players

Baseball Players


Additional Example 2C: Comparing Box-and-Whisker Plot

Course 2


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.


Basketball Players

Baseball Players



Course 2


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



Course 2


Which shoe store has a greater interquartile range?

Maroon’s shoe store has a longer box, so it has a greater interquartile range.



Sage’s Shoe Store


Check It Out: Example 2C

Course 2


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.



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.


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.



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.


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.


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.


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


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


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

do now 1.what percent of students chose math as their favorite class? hwk: 62, test on wednesday ch7...

Documents

data set

upper quartiles

lower quartiles

upper half

lower half

middle quartile

whisker plota box

set of dataupper quartile