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### Box-and-Whisker Plots

Making and Interpreting Box-and-Whisker Plots

Becky Afghani LBUSD Math Office 2003

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.

minimum

maximum

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

The minimum is 68.

The maximum is 100.

Step 3: Find the median of the data.

7 in the lower half

7 in the upper half

1 in the middle

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

The median is 85.

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

lower half

upper half

The middle number is not in the lower or upper half.

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

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

lower half

upper half

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

The lower quartile is 74.

Choral Response: What is the lower quartile?

The median of

the lower half

The median of

the lower half

The median of

the lower half

The median of

the lower half

The median of

the lower half

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

lower half

upper half

The middle number is not in the upper or upper half.

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

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

lower half

upper half

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

The upper quartile is 99.

Choral Response: What is the upper quartile?

The median of

the upper half

The median of

the upper half

The median of

the upper half

The median of

the upper half

The median of

the upper half

Now that we have our five-number summary, we can construct the box-and-whisker plot.

Minimum

68

Lower quartile (Q1)

74

Median (Q2)

85

Upper quartile (Q3)

99

Maximum

100

Write in Your Notes:What are the five items in the five number summary?

I can think

of one...

I bet

he knows!

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

50

60

70

80

90

100

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

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

Minimum

68

Lower quartile (Q1)

74

50

60

70

80

90

100

Median (Q2)

85

Upper quartile (Q3)

99

Maximum

100

Step 8: Draw a box between the lower and upper quartiles.

Minimum

68

Lower quartile (Q1)

74

50

60

70

80

90

100

Median (Q2)

85

Upper quartile (Q3)

99

Maximum

100

Step 9: Draw a vertical line through the median.

Minimum

68

Lower quartile (Q1)

74

50

60

70

80

90

100

Median (Q2)

85

Upper quartile (Q3)

99

Maximum

100

Step 10: Draw two “whiskers” from the quartiles to the minimum and maximum.

Minimum

68

Lower quartile (Q1)

74

50

60

70

80

90

100

Median (Q2)

85

Upper quartile (Q3)

99

Maximum

100

Interpreting the box-and-whisker plot

25%

25%

25%

25%

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.

Find the false statement.

50

60

70

80

90

100

74

99

85

100

68

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

4

2 3 6

1 1 1 2 4 4 5 5 6 6

5

6

0 1 2 4 9

42 is 42 years

Minimum and Maximum

Age at First Inauguration of

American Presidents from 1900 to 1999

4

2 3 6

1 1 1 2 4 4 5 5 6 6

5

6

0 1 2 4 9

42 is 42 years

42 is the minimum

69 is the maximum

Median

What is

halfway

between

54 and 55?

Age at First Inauguration of

American Presidents from 1900 to 1999

?

4

2 3 6

1 1 1 2 4 4 5 5 6 6

5

6

0 1 2 4 9

9th item

10th item

42 is 42 years

How many

data items

are there?

What is

half of 18?

54.5 is the median

18 items

Lower Quartile

Age at First Inauguration of

American Presidents from 1900 to 1999

4

2 3 6

54.5

1 1 1 2 4 4 5 5 6 6

5

6

0 1 2 4 9

42 is 42 years

How many

items are

in the lower

half?

9 items

Which item

is in the

middle?

The 5th item

51 is the lower quartile

Upper Quartile

Age at First Inauguration of

American Presidents from 1900 to 1999

4

2 3 6

54.5

1 1 1 2 4 4 5 5 6 6

5

6

0 1 2 4 9

42 is 42 years

How many

items are

in the upper

half?

The 5th item

9 items

Which item

is in the

middle?

60 is the upper quartile

The Box-and-Whisker Plot

Age at First Inauguration of

American Presidents from 1900 to 1999

4

2 3 6

54.5

5

1 1 1 2 4 4 5 5 6 6

40

50

6

0 1 2 4 9

60

70

42 is 42 years

Find the false statement.

40

50

60

70

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.

Average Monthly High Temperatures in Anchorage, Alaska

0

0

10

10

20

20

30

30

40

40

50

50

60

60

70

70

80

80

90

90

100

100

Average Monthly High Temperatures in Long Beach, California

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

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

Find the false statement.

Average Monthly High Temperatures in Long Beach, California

100

0

0

10

10

20

20

30

30

40

40

50

50

60

60

70

70

80

80

90

90

100

Average Monthly High Temperatures in Anchorage, Alaska

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.

In your notes...

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

2. Write a short description for each.

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