7th Grade Math

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Measures of Variation

PART A B

Multi-Part

Lesson 2

GLE 0706.5.4

Use descriptive statistics to

summarize and compare

data. SPI 0706.5.3 Calculate

and interpret the mean,

median, upper-quartile,

lower-quartile, and

interquartile range of a set

of data.

498 498 Statistical DisplaysStatistical Displays

Main Idea

Find the measures of

variation of a set of

data.

Vocabulary

measures of variation

range

quartile

lower quartile

upper quartile

interquartile range

outlier

Measures of Variation

SURVEYS Jamie asked her classmates how many

012345

Glasses of

Water Consumed

×

×

×

×

×

×

×

×

×

×

×

×

×

×

× ×

glasses of water they drink on a typical day.

1. What is the median of the data set?


2. Organize the data into two groups: the top
   half and the bottom half. How many data
   values are in each group?


3. What is the median of each group?


4. Find the difference between the two numbers from Exercise 3.

Measures of variation are used to describe the distribution of the data.

The range is the difference between the greatest and least data values.

Quartiles are values that divide the data set into four equal parts.

LQ median UQ

0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 5

⎧   ⎨^   ⎩ ⎧   ⎨   ⎩

The median of the lower

half of a set of data is

the lower quartile or

LQ; in this case, 1.

(^) The median of the upper
half of a set of data is
the upper quartile or
UQ; in this case, 3.5.
So, one half of the data lie between the lower quartile and upper
quartile. This is called the interquartile range.
Measures of Variation
Upper and Lower Quartiles
The upper and lower quartiles are the medians of the upper half and
lower half of a set of data, respectively.
14, 18, 19, 20, 24, 29, 31
lower quartile median upper quartile
Interquartile Range
The range of the middle half of the data. It is the difference between
the upper quartile and the lower quartile; in this case, 29 - 18 or 11.
The interquartile range is 29 - 18 or 11.
Range
The difference between the greatest and least data values; in this case,
31 - 14 or 17.
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