Boxandwhisker Diagram A boxandwhisker diagram is a line

Box-and-whisker Diagram A box-and-whisker diagram is a line segment showing the highest and lowest numbers, upper and lower quartiles, and median of a set of data.

Quartile A quartile is any one of three values that divide the data into four equally sized groups.

Lower Quartile The lower quartile is the median for the lower half of the data.

Middle Quartile The middle quartile is the median for all of the data.

Upper Quartile The upper quartile is the median for the upper half of the data.

Example 1 The following numbers represent the pages read yesterday by the twelve students in the class. Find the lower, middle, and upper quartiles: {16, 51, 29, 35, 70, 29, 40, 44, 39, 30, 50, 46}.

16, 29, 30, 35, 39, 40, 44, 46, 50, 51, 70 middle quartile: 39 + 40 = 39. 5 2 lower quartile: 29 + 30 = 29. 5 2 upper quartile: 46 + 50 = 48 2

Example 2 Construct a box-and-whisker diagram for the data in the last example. 16 29. 5 39. 5 48 70

Interquartile Range The interquartile range is the difference between the upper and lower quartile.

Example 3 Construct a box-and-whisker diagram for the following set of data, and calculate the interquartile range: {12, 32, 29, 35, 33, 17, 28, 24, 22, 25, 31}.

12, 17, 22, 24, 25, 28, 29, 31, 32, 33, 35 median: 28 lower quartile: 22 upper quartile: 32 interquartile range: 32 – 22 = 10 12 22 28 32 35

Example Use these data sets for the following problems: A = {13, 14, 16, 17, 18, 22, 25} B = {19, 22, 25, 37, 39, 40, 100}.

Example Find the median of each. A = {13, 14, 16, 17, 18, 22, 25} B = {19, 22, 25, 37, 39, 40, 100} A: 17; B: 36

Example Find the lower quartile of each. A = {13, 14, 16, 17, 18, 22, 25} B = {19, 22, 25, 37, 39, 40, 100} A: 15; B: 23. 5

Example Find the upper quartile of each. A = {13, 14, 16, 17, 18, 22, 25} B = {19, 22, 25, 37, 39, 40, 100} A: 22; B: 39. 5

Example Find the interquartile range of each. A = {13, 14, 16, 17, 18, 22, 25} B = {19, 22, 25, 37, 39, 40, 100} A: 7; B: 16

Example Construct a box-andwhisker diagram of A. 13 15 17 22 25

Example Construct a box-andwhisker diagram of B. 23. 5 19 39. 5 36 100

Stem-and-leaf Diagram A stem-and-leaf diagram is a type of bar graph in which the data points in each interval are listed in order.

Example 4 Make a stem-and-leaf diagram for the following set of data, which represents the number of pages read by twelve students: {16, 29, 30, 35, 39, 40, 44, 46, 50, 51, 70}.

Number of Pages Read 1 6 2 9 9 3 0 5 9 4 0 4 6 5 0 1 7 0

Example 5 Make a stem-and-leaf diagram for the following set of data: {120, 125, 129, 134, 138, 143, 149, 156, 159, 161}.

12 13 14 15 16 0 4 3 6 1 5 8 3 9 9 9

Example Make a stem-and-leaf diagram for the following set of scores on a fifty-point test: {32, 33, 37, 38, 42, 43, 44, 45, 45, 46, 47, 48, 49, 50, 50}. 3 2 3 7 8 4 2 3 3 4 4 5 5 5 6 7 8 9 5 0 0 0

Scatterplot A scatterplot is a graphical representation of the relationship of two variables in the form of ordered pairs of points plotted in a coordinate plane.

h 65 63 72 64 70 70 w 160 145 180 150 220 180 h 64 70 76 71 73 63 w 130 170 180 200 210 150 h 61 66 66 70 66 68 w 120 145 155 175 160 170

Weight (in pounds) Height vs. Weight Height (in inches)

Correlation refers to the relationship between the variables in a scatterplot. Correlation can be positive or negative.

Hours/Week of TV GPA 4 3. 7 8 3. 5 11 3. 0 10 2. 8 15 2. 7 12 2. 6 20 2. 6 18 2. 4 25 1. 9 20 1. 5 15 1. 3 25 1. 1

GPA TV and GPA Hours/Week of TV

Example 6 Construct a scatterplot for the following data, which relates the number of exercise minutes per day (m) to a person’s heart rate (r). What does the graph show? State whether the correlation seems to be positive or negative.

m 5 r 92 30 75 15 78 10 90 45 70 12 88 m 40 r 74 60 68 35 76 20 76 8 78 25 76

Average Heart Rate Exercise and Heart Rate Minutes of Exercise/Day

The scatterplot shows that the heart rate r decreases as one exercises more. The correlation is negative.

Reaction Time (in sec) Alcohol Consumption and Reaction Times Alcohol Consumed (in ounces)

Reported Work Injuries per Year Education and Work Injuries Years of Education

Achievement Scores Anxiety vs. Achievement Anxiety Level