6th Grade Math Textbook, Fundamentals

212 Chapter 8

8-3

Name Number of Films Seen

Elena 11

Ray 13

James 8

Inez 104

Li 16

Lamar 10

Remember:The median

of an even set of numbers

is the mean of the two

middle numbers.

The outlier increases the median of the data by 1.

If the outlier is one extreme value, it can never affect the mode because

it would not occur more often than any other value in the data set.

Therefore, the outlier does not change the mode of the data.

To find the range:

Interpret Data

Objective To examine how outliers in a set of data affect the mean, median, and mode

• To use range as a measure of dispersion• To use statistics to make estimates• To organize
  data using a spreadsheet

Six students are taking a film class. The table shows how many
films each student has seen so far this year. One number
greatly differs from the others. How does it affect the
statistical measures you would use to describe the data set?

To find how one number affects the statistical measure

of a set of data, find the mean, median, mode, and range

with and without that number.

Numbers in a data set that are much greater or much

less than others in the set are called. An outlier

is an extreme value.

The outlier for the number of films watched is 104.

Outliers affect some measures of central tendency

more than others.

To find the mean:

outliers

With outlier

 27

The mean is 27.

To find the median:

With outlier

8, 10, 11, 13, 16, 104

 12

The median is 12.

Without outlier

11.6

The mean is 11.6.

Without outlier

8, 10, 11, 13, 16

The median is 11.

11  13  8  16  10

5

11  13  8  104  16  10

6

11  13

2

58

5

162

6

The outlier increases the mean of the data by 15.4.

With outlier

104  8  96

The range is 96.

Without outlier

16  8  8

The range is 8.

The outlier increases the range of the data by 88.

• Outliers have the greatest effect on the
  mean and range of a data set.


• The median gives the best description
  of a data set that contains an outlier.