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Box-and-Whisker Plots

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Box-and-Whisker Plots

Making and Interpreting Box-and-Whisker Plots

Becky AfghaniLBUSD Math Office2003

Construct and

Interpret

Box and Whisker Plots

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.

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.

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.

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

Minimum

?

Lower quartile (Q1)

?

Median (Q2)

?

Upper quartile (Q3)

?

Maximum

?

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

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.

To find the

minimum...

To find the

maximum...

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.

To find the

median...

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

lower half

upper half

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

The lower quartile is 74.

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

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

lower half

upper half

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

The upper quartile is 99.

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

Minimum

68

Lower quartile (Q1)

74

Median (Q2)

85

Upper quartile (Q3)

99

Maximum

100

I can think

of one...

I bet

he knows!

50

60

70

80

90

100

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

Minimum

68

Lower quartile (Q1)

74

50

60

70

80

90

100

Median (Q2)

85

Upper quartile (Q3)

99

Maximum

100

Minimum

68

Lower quartile (Q1)

74

50

60

70

80

90

100

Median (Q2)

85

Upper quartile (Q3)

99

Maximum

100

Minimum

68

Lower quartile (Q1)

74

50

60

70

80

90

100

Median (Q2)

85

Upper quartile (Q3)

99

Maximum

100

Minimum

68

Lower quartile (Q1)

74

50

60

70

80

90

100

Median (Q2)

85

Upper quartile (Q3)

99

Maximum

100

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.

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.

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

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

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

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

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

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

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

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.

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

2. Write a short description for each.