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Math Foundations

When to use (and calculate) the mean, median, or mode of a given data set is determined.

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After completing this tutorial, you will be able to complete the following:

- Calculate mean, median, and mode.
- Determine the appropriateness of using mean, median, and mode to solve problems.

Mean is synonymous with the word average.

To find the mean, you follow the same process as finding the average. Add all the digits in the data set and divide the sum by the amount of values in the data.

For example, to find the mean of the data set 39, 37, 36, 37, 36, 41, 40, you should add all these numbers and divide by 7 because there are 7 numbers in the data set.

The mean is 38.

Finding the mean is a multi-step process. It is important to remember that to find the mean, you must add and divide.

The median is the middle value of a set of data.

To find the median, the numbers in the set must be in numerical order. The median is the number in the middle, when the data set is in numerical order.

For example, using the data set above, first put the numbers in order: - notice that 37 is in the middle, therefore 37 is the median.

More steps are required to find the median, when there is an even amount of numbers in the data set.

If there were 6 numbers instead of 7, in the data set above, there would be two numbers in the middle. In order to find the median, you need to add the two middle numbers and divide by two.

For example:

The numbers in the middle would be 37 and 39. To find the median add 37 and 39 and divide by 2, which basically means that you will be finding the mean of the two middle numbers

The median is 38.

The mode is the data value that occurs the most.

To find the mode, just find the number that occurs the most.

For example in the data set 36, 36, 37, 37, 39, 40, 41, we identify which number(s) occur the most. The numbers that appear the most are 36 and 37; therefore, 36 and 37 are the mode.

There can be one mode, no mode, or more than two modes. If all the numbers occur the same amount of times then there is no mode.

Working with word problem.

In the Activity Object, the mean, median and mode problems are presented as word problems. Because of this, the following key words or phrases should be used to identify which type of data needs to be calculated.

mean - "average," "equally divided," "equally distributed"

median - "middle," "the value which is smaller than half and greater than the other half"

mode - "most" "most frequent"

The following key vocabulary terms will be used throughout this Activity Object:

- mean - the average; the sum of the data values divided by the number of data values
- median - the middle number of a data set when the numbers are arranged from least to greatest
- mode - the most repeated data value

Approximate Time | 15 Minutes |

Pre-requisite Concepts | Students should understand how to calculate mean, median, and mode. |

Course | Math Foundations |

Type of Tutorial | Skills Application |

Key Vocabulary | mean, median, mode |