Box-and-Whisker Plots

Important TermsMedian: The middle number in a set of data when the data

are arranged in numerical order.

Quartile: One of four equal parts of data from a large set of data.

Upper Quartile: The median of the upper half of a set of numbers.

Lower Quartile: The median of the lower half of a set of numbers.

Lower Extreme: The least number in a set of data.

Upper Extreme: The greatest number in a set of data.

Outliers: Data that is more than 1.5 times the inner quartile range, from the quartiles.

Step 1

Put the data in order from the least to the greatest.

Data: Automobile gas mileages

12 17 19 20 22 23 24 24 27

29 31 34 39 45 48

27 12 23 45 24 39 19 48 24 20 22 29 17 34 31

Find the median - 24

Step 2

Find the median of the first half of the data

12 17 19 20 22 23 24 24 27 29 31 34 39 45 48

20

This is called the Lower Quartile

LQ -

Step 3

Find the median of the upper half of the data

12 17 19 20 22 23 24 24 27 29 31 34 39 45 48

34

This is called the Upper Quartile

UQ -Inter Quartile Range - the difference

between the UQ and the LQ

34 - 20 = 14IR = UQ - LQ

Step 4aFind the lowest number

12 17 19 20 22 23 24 24 27 29 31 34 39 45 48

12

This is called the Lower Extreme

LE -

Find the highest number

This is called the Upper Extreme

48UE -

Step 4b

Step 512 17 19 20 22 23 24 24 27 29 31 34 39 45 48

Draw and label a number line with your 5 points.

€

10 16 22 28 34 40 46

• • • ••LE UEUQLQ Median

Step 5 continued

Draw a box starting at the lower quartile and ending at the upper quartile.

€

10 16 22 28 34 40 46

• • • ••

Draw a vertical line through the median value.

Step 5 continued

Draw a line from the lowest number to the lower quartile and one from the highest number to the upper quartile.

€

10 16 22 28 34 40 46

• •

“The Whiskers”

A box - and - whisker plot divides data into four equal parts that represent 25% of the data

€

10 16 22 28 34 40 46

• •

25% of the data falls between the LE and the LQ.

25% of the data falls between the LQ and the median.

25% of the data falls between the median and the UQ.

25% of the data falls between the UQ and the UE.

You Try It!

Make a box-and-whisker plot for the following recent test scores.

98 75 69 96 85 74 98 79 83 90 62 74 84 86

62 69 74 74 75 79 83 84 85 86 90 96 98 9883.5

Note: Because there is an even number of data, you have to take the average of the two middle numbers to determine the median.

Median - 83.5

Lower Quartile - 74

Upper Quartile - 90

Lower Extreme - 62

Upper Extreme - 98

50 60 70 80 90

€

100

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