6th Grade Math Textbook, Fundamentals

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8-2

Measures of Central Tendency

and Range

Objective To find median, mean, mode, and range• To choose

the best measure of central tendency to represent a set of data• To find

a missing value of a set of numbers, given its mean, median, or mode

The salaries of five starting players on a professional basketball
team are $650,000, $580,000, $710,000, $780,000, and $540,000.
How can you best represent this set of data?

To find how you can best represent this set of data, choose one

of the measures of central tendencyor use the rangeof that

set of data.

The are mean, median, and mode.

• The is a type of statistical average. To find the mean of a
  set of data, divide the sum of all the numbers in the set by the number
  of items. The mean is most useful when the data are close together.

$652,000

The mean of the salaries is $652,000.

• The is the middle value or average of two middle values of a set
  of data that are arranged in order. To find the median, list the values in
  order, and identify the middle value. For a set with an even number of
  values, the median is the mean of the two middle numbers. The median is
  most useful when the data contain extremely high or extremely low values.
  $540,000 $580,000 $650,000 $710,000 $780,000
  The median salary is $650,000.


• The is the item that occurs most frequently in the data. A data set may
  have no mode, one mode, or more than one mode. When there is no value that
  repeats, there is no mode. The mode is most useful when many items in the
  data set have the same value. The mode is the only appropriate measure for
  non-numeric data—for example, when considering the votes for favorite
  school mascot.


• The is the difference between the greatest and least values in a data set.
  $780,000 $540,000 $240,000 The range of the salaries is $240,000.

Certain measures of central tendency sometimes represent the data better than others.

The measure(s) closest to most of the data most accurately represent(s) that data.

• The mean, $652,000, is $128,000 less than the greatest salary and $112,000
  more than the least salary, so the salaries are fairly close together. The mean
  is appropriate in representing this data set.


• Since the values do not repeat, there is no mode.


• The range does not tell you what most of the players are being paid.


• The median, $650,000, is close to most of the data values and is appropriate
  in representing the data set.

range

mode

You can list either from least to

greatest or greatest to least.

$3,260,000

5

$650,000 $580,000 $710,000 $780,000 $540,000

5

median

mean

measures of central tendency