Mean, Median, Mode

Mean, Median, Mode

Objective: Derive and understand the mean, median and mode given a set of data.

​Vocabulary

​Central Tendency: A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data.

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​Example: Your grade for the marking period is a measure of central tendency of ALL your grades together.

Mean

• A measure of the central tendency of a data set

• Also called the average

• Add together all of the numbers, then divide by the number of numbers

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​Example:

​Find the mean of the following data values: 12, 9, 5, 10, 6, 13, 9, 8

Fill in the Blanks

Find the mean of these numbers:
2, 57, 38, 42, 6

Median

• A measure of central tendency

• The middle number in a data set

• Order all of the numbers from least to greatest

• If there is an odd number of numbers, find the middle number

• If there is an even number of numbers, find the mean of the two middle numbers

​Examples

Find the median of the following data values: 13, 11, 2, 13, 3, 14, 7, 5

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​Find the median of the following data values: 100, 2, 34, 75, 6, 83, 12

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Fill in the Blanks

What is the median?

5, 22, 81, 16, 15, 22

Fill in the Blanks

Find the median of these numbers: 2, 57, 38, 42, 6

Mode

• A measure of central tendency

• Tells us which number occurs most often

• Find the number that repeats the most in the data set

• There can be more than one mode if multiple numbers repeat the same number of times

• There can be no mode if none of the numbers repeat

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​Example:

​Find the mode of the following data values: 12, 10, 9, 5, 10, 6, 11, 1 3, 9, 8, 12, 9

Fill in the Blanks

At Donald's Donuts the number of donut holes in a bag can vary. Help Donald find the mode.

(if there is no mode, type none)

12, 10, 10, 10, 13, 12, 11, 13, 10

Range

• Tells us how spread out the data is

• Subtract the smallest number from the largest number

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​Example:

​Find the range of the following data values: 13, 11, 2, 13, 3, 15, 7, 6

Fill in the Blanks

Find the Range: 98, 74, 67, 98, 99, 102, 95

Outlier

Values that are very low or high relative to the other values in a list of values. If you have many houses in a neighborhood in the $250K–300K range and then one mansion that is valued at $3M, we would call the value of the mansion an “outlier” in our set of data.

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The methods for determining whether or not a value is truly an outlier are beyond the scope of this lesson but I wanted you to at least be familiar with the term.