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Objective

Find the mean of a set of data

Vocabulary

Average

The sum of the data divided by the number of pieces of data

Also called the “mean”

Vocabulary

Measure of central tendency

A number that helps describe all of the data in a data set

Most common

Mean

Median

Mode

Vocabulary

Mean

The sum of the data divided by the number of pieces of data

Also called the “average”

Vocabulary

Outlier

A value much higher or lower than the other values

80, 81, 40, 77, 82

40 is the outlier

Example 1 Find Mean

Example 2 Determine How Outliers Affect Mean

READING The number of words per sentence on one page of a novel is shown in the table. Find the mean.

Words per Sentence 8 11 9 710 7 8 8 9 18 7 8 7 11 7 9

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Mean = sum of datapieces of data Add the data in each column

34 + Mean = 47 +31 +32Put sum of columns in equation

Count the number of pieces of data and put in the denominator

16

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Mean = sum of datapieces of data

Follow order of operations rules

Mean = 144

16Mean = 34 + 47 + 31 + 32

P E MD AS

Remember fraction bar is used as enclosures

Add the numeratorBring down 16

16Divide 144 by 16

Mean = 9

Answer: Mean = 9 words

PRACTICE The number of days per week that members of the middle school band practice their instrument is shown in the table. Find the mean.

Days of Practice6 7 5 5 3 6 5 1 4 6 7 5

Answer: Mean = 5 days per week

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BASKETBALL Find the mean with and without the outlier. Then describe how the outlier affects the mean.

Points per Game98 102 88 7678 44 98 101100 77 108 86

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Determine the outlier

Must find 2 means - with and without the outlier

mean with outlier

Points per Game98 102 88 7678 44 98 101

100 77 108 86

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Add the data in each column

Put sum of columns in equation

Mean = 276 +223 +294 + 263

Count the number of pieces of data and put in the denominator

12

mean with outlier

Points per Game98 102 88 7678 44 98 101

100 77 108 86

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Mean = 276 +223 +294 + 263 12 Follow order of operations

rulesP E MD AS

Add the numeratorBring down 12

Mean = 1056 12

Divide 1056 by 12Mean = 88

Points per Game98 102 88 7678 44 98 101

100 77 108 86

mean without outlier

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Add the data in each column

Put sum of columns in equation

Mean = 276 +179 +

Do not add the outlier of 44

294 +263

Count the number of pieces of data and put in the denominator (remember don’t count the outlier)

11

Points per Game98 102 88 7678 44 98 101

100 77 108 86

mean without outlier

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Mean = 276 +179 +294 +263 11

Follow order of operations rules

P E MD ASAdd the numerator

Mean = 1012

Bring down 11

11

Divide 1012 by 11Mean = 92

Answer: The outlier lowered the mean by 4 points

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Mean with outlier = 88

Mean without outlier = 92

Describe how the outlier affects the mean

The outlier was 44 which was lower than the other data so without the outlier the mean was higher than with the outlier

EXAM SCORES Find the mean with and without the outlier. Then describe how the outlier affects the mean.

Exam Scores84 75 93 8236 74 79 91

Answer: mean with outlier: 76.75; mean without outlier: 82.57; The outlier lowers the mean of the data by about six points.

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Assignment Lesson 2:6 Mean 9 - 18 All