Box-and-Whisker Plots

Making and Interpreting Box-and-Whisker Plots

Becky Afghani LBUSD Math Office 2003

You will:

Construct andInterpret

Box and Whisker Plots

What is a Box-and Whisker Plot?

• Suppose you have a large set of data and want to know how it is distributed.

• Think of a teacher’s class set of test scores.

• A box-and-whisker plot displays the median, the quartiles, and the greatest and least values.

Why use a Box-and Whisker Plot?

• The box-and-whisker plot is a visual way to show the data.

• The median and quartiles can easily be read.

• The shape of the box and the whiskers gives information about how the numbers are spread out.

Who uses Box-and Whisker Plots?

• Scientists who perform experiments display their results using box-and-whisker plots.

• Medical researchers display their findings using box-and-whisker plots.

• Anyone who reads a scientific report needs to understand how a box-and-whisker works.

We will make a Box-and Whisker Plot

Here are all of the test scores from your class on the last math test.

(Not really!)

87 75 83 94 100

74 68 98 99 85

83 100 72 68 100

You will need a five-number summary in order to construct the box-and-

whisker plot.Minimum

Lower quartile (Q1)Median (Q2)

Upper quartile (Q3)Maximum

?????

Step 1: Write the data in order from least to greatest.

87 75 83 94 100

74 68 98 99 85

83 100 72 68 100

68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

Step 2: Find the minimum and maximum values of the

data.68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100,

100

minimumThe minimum is 68.

maximum

The maximum is 100.The 5 number Summary

Minimum

1st (lower) quartile

Median(2nd Q)

3rd (upper) quartile

Maximum

Tell your neighbor how to find the minimum and

maximum.To find the

maximum...To find theminimum...

Step 3: Find the median of the data.

68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

7 in the upper half

7 in the lower half

1 in the middle

The median is 85.

The 5 number Summary

Minimum 68

1st (lower) quartile

Median(2nd Q)

3rd (upper) quartile

Maximum

Tell your neighbor how to find the median.

To find themedian...

Step 4: Find the lower quartile (Q1) of the data.

68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

upper halflower half

The middle number is not in the lower or

upper half.

Step 4: Find the lower quartile (Q1) of the data.

68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

upper halflower half

The lower quartile is 74.

Choral Response: What is the lower quartile?

The median ofthe lower half

The median ofthe lower half

The median ofthe lower half

The median ofthe lower halfThe median of

the lower half

Step 5: Find the upper quartile (Q3) of the data.

68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

upper halflower half

The middle number is not in the upper or

Lower half.

Step 5: Find the upper quartile (Q3) of the data.

68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

upper halflower half

The upper quartile is 99.

Choral Response: What is the upper quartile?

The median ofthe upper half

The median ofthe upper half

The median ofthe upper half

The median ofthe upper halfThe median of

the upper half

Now that we have our five-number summary, we can

construct the box-and-whisker plot.

MinimumLower quartile

(Q1)Median (Q2)Upper quartile (Q3)

Maximum

68748599

100

Write in Your Notes:What are the five items in

the five number summary?

I can thinkof one...

I bethe knows!

Step 6: Draw a number line that can show the data.

68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

50 60 70 80 90 100

Step 7: Mark the minimum, maximum, median and both quartiles on the number line.

50 60 70 80 90 100

Minimum

Lower quartile (Q1)

Median (Q2)

Upper quartile (Q3)

Maximum

68

74

85

99

100

Step 8: Draw a box between the lower and upper

quartiles.

50 60 70 80 90 100

MinimumLower quartile

(Q1)Median (Q2)Upper quartile (Q3)

Maximum

68748599

100

Step 9: Draw a vertical line through the median.

50 60 70 80 90 100

MinimumLower quartile

(Q1)Median (Q2)Upper quartile (Q3)

Maximum

68748599

100

Step 10: Draw two “whiskers” from the quartiles

to the minimum and maximum.

50 60 70 80 90 100

MinimumLower quartile

(Q1)Median (Q2)Upper quartile (Q3)

Maximum

68748599

100

Interpreting the box-and-whisker plot

50 60 70 80 90 100

Remember these are test scores.

25% of the test scores are in each whisker and each section of the box.

25% 25% 25% 25%

Find the false statement.

50 60 70 80 90 100

68 74 85 99

100

A) One fourth of the test scores were between 85 and 99.

B) One half of the test scores were between 74 and 99.

C) One half of the test scores were between 85 and 100.

D) Three fourths of the test scores were between 68 and 85.

Make another box-and-whisker plot from this

data:Age at First Inauguration of

American Presidents from 1900 to 1999

456

2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 942 is 42

years

Minimum and Maximum

42 is the minimum

69 is the maximum

Age at First Inauguration of American Presidents from 1900 to

1999

456

2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 942 is 42

years

MedianAge at First Inauguration of

American Presidents from 1900 to 1999

456

2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 942 is 42

years

How manydata itemsare there?

18 items

What ishalf of 18?

9th item

10th item

?

What ishalfwaybetween

54 and 55?

54.5 is the median

Lower Quartile

Age at First Inauguration of American Presidents from 1900 to

1999

456

2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 942 is 42

years

54.5

How manyitems are

in the lowerhalf?

9 itemsWhich item

is in themiddle?

The 5th item

51 is the lower

quartile

Upper Quartile

Age at First Inauguration of American Presidents from 1900 to

1999

456

2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 942 is 42

years

54.5

How manyitems are

in the upperhalf?

9 itemsWhich item

is in themiddle?

The 5th item

60 is the upper

quartile

The Box-and-Whisker Plot

40 50 60 70

Age at First Inauguration of American Presidents from 1900 to 1999

456

2 3 61 1 1 2 4 4 5 5 6 60 1 2 4 9

42 is 42 years

54.5

Find the false statement.

A) The oldest president at his inauguration was 69.

B) One fourth of the presidents were 60 or over when inaugurated.

C) One half of the presidents were inaugurated between ages 50 and 60.D) The youngest president to be inaugurated in the 1900s was 42.

40 50 60 70

Multiple Box-and-Whisker Plots Can Be Used to Compare Data

0 10 20 30 40 50 60 70 80 90 100

Average Monthly High Temperatures in Anchorage, Alaska

0 10 20 30 40 50 60 70 80 90 100

Average Monthly High Temperatures in Long Beach, California

Describe the variability between the data sets and compare the two 5 number summaries

Find the false statement.

A) The range of average monthly high temperatures is broader in Anchorage than in Long Beach.

B) The average monthly high temperatures in Long Beach are warmer than Anchorage.C) Half of the average monthly highs in Long Beach are between 27 and 59 degrees.

0 10 20 30 40 50 60 70 80 90 100

Average Monthly High Temperatures in Anchorage, Alaska

0 10 20 30 40 50 60 70 80 90 100

Average Monthly High Temperatures in Long Beach, California

In your notes...

1. List the five items required for a box-and-whisker plot.

2. Write a short description for each.