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. Box-and-whisker Diagram

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

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

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

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

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}.

= , 29, 29, 30, 35, 39, 40, 44, 46, 50, 51, 70 middle quartile: = 29.5 lower quartile: = 48 upper quartile:

Construct a box-and-whisker diagram for the data in the last example Example 2

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

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}. 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}. Example 3

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

Use these data sets for the following problems: A = {13, 14, 16, 17, 17, 18, 22, 22, 25} B = {19, 22, 25, 35, 37, 39, 40, 100}. Use these data sets for the following problems: A = {13, 14, 16, 17, 17, 18, 22, 22, 25} B = {19, 22, 25, 35, 37, 39, 40, 100}. Example

Find the median of each. A: 17; B: 36 A = {13, 14, 16, 17, 17, 18, 22, 22, 25} B = {19, 22, 25, 35, 37, 39, 40, 100} A = {13, 14, 16, 17, 17, 18, 22, 22, 25} B = {19, 22, 25, 35, 37, 39, 40, 100} Example

Find the lower quartile of each. A: 15; B: 23.5 A = {13, 14, 16, 17, 17, 18, 22, 22, 25} B = {19, 22, 25, 35, 37, 39, 40, 100} A = {13, 14, 16, 17, 17, 18, 22, 22, 25} B = {19, 22, 25, 35, 37, 39, 40, 100} Example

Find the upper quartile of each. A: 22; B: 39.5 A = {13, 14, 16, 17, 17, 18, 22, 22, 25} B = {19, 22, 25, 35, 37, 39, 40, 100} A = {13, 14, 16, 17, 17, 18, 22, 22, 25} B = {19, 22, 25, 35, 37, 39, 40, 100} Example

Find the interquartile range of each. A: 7; B: 16 A = {13, 14, 16, 17, 17, 18, 22, 22, 25} B = {19, 22, 25, 35, 37, 39, 40, 100} A = {13, 14, 16, 17, 17, 18, 22, 22, 25} B = {19, 22, 25, 35, 37, 39, 40, 100} Example

Construct a box-and- whisker diagram of A Example

Construct a box-and- whisker diagram of B Example

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

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

Number of Pages Read

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

Make a stem-and-leaf diagram for the following set of scores on a fifty-point test: {32, 33, 37, 38, 42, 43, 43, 44, 44, 45, 45, 45, 46, 47, 48, 49, 50, 50, 50} Example

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. Scatterplot

hh ww hh ww hh ww

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

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

Hours/Week of TV 4488 GPA

Hours/Week of TV GPA TV and GPA

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. Example 6

mm rr mm rr

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

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

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

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

Anxiety Level Achievement Scores Anxiety vs. Achievement