Lesson 13-5

Box-and-Whisker Plots

Click the mouse button or press the Space Bar to display the answers.

Objectives

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Organize and use data in box and whisker plots

•

Organize and use data in parallel box and whisker plots

Vocabulary

•

Box and whisker plot

–

•

Extreme values

–

Box-and-Whiskers Plot

•

Parts of the Plot:

– – –

Smallest data value (not an outlier) Largest data value (not an outlier) whiskers part Quartiles 1, 2 and 3 (Q1, Q2 also known as median, Q3) box part

•

Outliers – any data value that is outside the following range: [Q1 – 1.5



IQR, Q3 + 1.5



IQR] smallest* Q1 Q2 Q3 largest* * - not an outlier

Example 1a

Ecology The average water level in Lake Travis in central Texas during August is a good indicator of whether the region has had normal rainfall, or is suffering from a drought. The following is a list of the water level in feet above sea level during August for the years 1990 to 2000.

674

,

673

,

678

,

673

,

670

,

677

,

653

,

679

,

664

,

672

,

645

Draw a box-and-whisker plot for these data.

Example 1a cont

Step 1 Determine the quartiles and any outliers.

Order the data from least to greatest. Use this list to determine the quartiles.

645 , 653 , 664 , 670 , 672 , 673 , 673 , 674 , 677 , 678 , 679 Determine the interquartile range.

Check to see if there are any outliers.

Any numbers less than 644.5

than 696.5

or greater are outliers. There are none.

Example 1a cont

Step 2 Draw a number line.

Assign a scale to the number line that includes the extreme values. Above the number line, place bullets to represent the three quartile points, any outliers, the least number that is

not

an outlier, and the greatest number that is

not

an outlier.

645 664 673 679 677

Example 1a cont

Step 3 Complete the box-and whisker plot.

Draw a box to designate the data between the upper and lower quartiles. Draw a vertical line through the point representing the median. Draw a line from the lower quartile to the least value that is

not

an outlier. Draw a line from the upper quartile to the greatest value that is

not

an outlier.

Example 1b

What does the box-and-whisker plot tell about the data?

Notice that the whisker and the box for the top half of the data is shorter than the whisker and box for the lower half of the data.

Answer:

The upper half of the data are less spread out than the lower half of the data; data is skewed left.

Example 2

Climate Pilar, who grew up on the island of Hawaii, is going to go to college in either Dallas or Nashville. She does not want to live in a place that gets too cold in the winter, so she decided to compare the average monthly low temperatures of each city.

Draw a parallel box-and-whisker plot for the data.

Determine the quartiles and outliers for each city.

Average Monthly Low Temperatures (



F) Month Dallas Nashville

Jan.

Feb.

Mar.

Apr.

May June July Aug.

Sept.

Oct.

Nov.

Dec.

32.7

36.9

45.6

54.7

62.6

70 74.1

73.6

66.9

55.8

45.4

36.3

26.5

29.9

39.1

47.5

56.6

64.7

68.9

67.7

61.1

48.3

39.6

30.9

Example 2 cont

Dallas

32.7

, 36.3

, 36.9

, 45.4

, 45.6

, 54.7

, 55.8

, 62.6

, 66.9

, 70 , 73.6

, 74.1

Nashville

26.5

, 29.9

, 30.9

, 39.1

, 39.6

, 47.5

, 48.3

, 56.6

, 61.1

, 64.7

, 67.7

, 68.9

Neither city has any outliers.

Draw the box-and-whisker plots using the same number line.

Answer:

Example 2 cont

Use the parallel box-and-whisker plots to compare the data.

Answer:

The interquartile range of temperatures for both cities is about the same. However, all quartiles of the Dallas Temperatures are shifted to the right of those of Nashville, meaning Dallas has higher average low temperatures.

Summary & Homework

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Summary:

–

The vertical rule in the box of a box-and-whisker plot represents the median

–

The box of a box-and-whisker plot represents the interquartile range

–

The bullets at each end of a box-and-whisker plot are the extremes

–

Parallel box-and-whisker plots can be used to compare data

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Homework:

–

pg 740 10-26 even