Notes Measures of Variation Range and Interquartile Range

8/12/2019 Notes Measures of Variation Range and Interquartile Range

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Name__________________________________________________________Advisory_____________

Notes and Classwork: Measures of Variation

A measure of variabilityis a number that represents how spread out a set of data is. (Synonyms for

variability are variation, dispersion, or spread) There are three measures of variability that we will focus on:

range, interquartile range and the mean absolute deviation (MAD).

MEASURES OF VARIABILITY

RANGE

Range- The range is the difference between the largest piece of data and the smallest piece of data.

The range is the most basic calculation of variability.

To find the range:

The range is found by subtracting the smallest data value from the largest data value in the set.

RANGE

INTERQUARTILE

RANGE

MEANABSOLUTEDEVIATION(To be covered in next set of

notes


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Example 1:

Find the range of scores in the two advisories below.

Harvard 6 98, 75, 61, 88, 80, 97, 72, 92, 81, 78

Amherst 6 92, 92, 90, 95, 88, 85, 88, 50, 80, 96

The range of scores in Harvard 6 is _______________________________________.

The range of scores in Amherst 6 is ______________________________________.

What does this number represent? How are the scores for each of the two advisories different?

Does the range accurately describe these differences?

Stop and jot with your partner.


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Example 2:

You decide to go swimming at M Street Beach over the weekend. The data below represents the

ages of the people at the beach on Saturday and Sunday.

Saturday Sunday8, 13, 7, 8, 5, 15, 16, 18, 6, 10, 75, 20, 12, 13 20, 35, 40, 38, 19, 29, 60, 48, 19, 30, 25, 28

What was the range of ages at the M Street Beach on Saturday?

What was the range of ages at the M Street Beach on Sunday?

Look at this data. What does the range tell us? What does the range NOT tell us? Stop and jot

with your partner.


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INTERQUARTILE RANGE

Interquartile Range- This measure of variability breaks the data up into 4 groups: the upper

quartile, lower quartile, upper extreme and the lower extreme. The interquartile range (IQR) finds

the difference between the upper and lower quartiles.

To find the interquartile range:

1) Order the data from least to greatest.2) Find the median of the data.3) If the median is a value in the set, put a box around it.

OR

If the median is not a value in the set, place a line between the two pieces of data that it falls

between.

4) Find the median of the data above the median. This is the upper quartile. Circle it.5) Find the median of the data below the median. This is the lower quartile. Circle it.6) Find the difference between the upper and lower quartiles. This is the interquartile range.

Whew! That is a lot of steps! Wait

until we get to calculating the mean

absolute deviation


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Example 1:

Find the interquartile range of the math scores below.

90, 85, 88, 70, 78, 65, 68

Complete steps 1, 2 and 3.

Complete steps 4, 5 and 6.

The IQR for the math scores is _______________________.

To find the interquartile range:

1) Order the data from least to greatest.

2) Find the median of the data.

3) If the median is a value in the set, put

a box around it.

OR

If the median is not a value in the set,

place a line between the two pieces of

data that it falls between.

4) Find the median of the data above the

median. This is the upper quartile.

Circle it.

5) Find the median of the data below the

median. This is the lower quartile.

Circle it.

6) Find the difference between the

upper and lower quartiles. This is the

interquartile range.


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Now, what does this actually mean? Stop and jot with your partner.

Example 2:

Ms. Adam is turning into a crotchety old lady and yells at cars as they drive by BCCS. She also

calculates the speed in miles per hour of cars as they drive by. Here are the speeds: 12, 8, 10, 25,

30, and 25.

The interquartile range of speeds passing by BCCS is __________________________________.


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The interquartile range is often preferred over the range because it eliminates any outliers. It shows

how spread apart the middle 50% of the data is.

Lets make sure weve got this

7, 13, 14, 15, 16, 45, 70

The median value, the lower quartile value and the upper quartile value split the data into quarters,

or four equal groups.

Example 3:

Find the IQR of the data below.

Hours Slept by 6thGrade Teachers 8, 7, 7, 8, 7, 9, 2, 6

Median: __________

Lower Quartile: __________

Upper Quartile: __________

IQR: __________

Upper

Extreme

Median-

splits data

in half

Lower

Extreme

Lower Quartile Upper Quartile


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Precision Practice.

Find the Interquartile Range of the data sets below.

1) 2, 2, 4, 5, 6, 6, 7

2) 13, 11, 12, 12, 12, 10, 11

3) 20, 18, 30, 22, 15, 16, 75, 28

4)

50, 30, 15, 25, 40, 10


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A visual called a box and whiskers plot, or box plotallows us to see how spread out the data is

within quartiles.

Although you cannot determine exact values from a box plot, you are able to use percents to

describe how the data is distributed.

Example 4:

Use the box and whiskers plot to answer the questions that follow.

1) What is the interquartile range shown above? __________2) What percent of the class earned at least a 50? __________3) What fraction of students earned less than a 50. __________4)Which quarter of the data is most spread out? Between ________and __________.


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Example 5:

Use the box plot to answer the questions that follow.

1) What is the upper quartile? ____________

2) What is the median mileage logged? ____________

3)What is the highest weekly total? ____________

4)What percent of runners run less than 40 miles per week? ____________

5) How many runners run less than 20 miles in a week? ____________

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Notes Measures of Variation Range and Interquartile Range