# Statistical Variation

## Overview

The **center** of a numerical data set summarizes all of the values with one number.

Mathematicians often use mean or median to calculate the center of their data set.

Mean | Median |

The mean is the average. | The median is the middle value. |

Add all of the numbers in a data set and then divide the sum by the total number of data points. |
Order the numbers in a data set from least to greatest. Identify the number that falls in the middle. |

data set: 6, 8, 6, 8, 7, 4, 3 6 + 8 + 6 + 8 + 7 + 4 + 3 = 42 42 ÷ 7 = 6 mean = 6 |
data set: 6, 8, 6, 8, 7, 4, 3 3, 4, 6, 6, 7, 8, 8 median = 6 |

The **variation** uses one number to describe how all of the values are different. The most basic measure of variation is range.

Range |

The range is the difference between the highest and lowest value in a data set. Subtract the lowest value from the highest value. 6, 8, 6, 8, 7, 4, 3 8 – 3 = 5 range = 5 |

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Use the data set below to answer question.

75, 56, 77, 82, 90

Use mean to determine the center of the data set.

76

First add all of the data values: 75 + 56 + 77 + 82 + 90= 380.

Then divide the sum by the total number of values:

Use the data set below to answer question.

90, 92, 96, 95, 92

Use range to determine the variation of the data set.

6

Subtract the smallest value from the largest value. 96 – 90 = 6

Use the data set below to answer question.

90, 92, 96, 95, 92

Use median to determine the center of the data set.

92

First order the numbers from least to greatest: 90, 92, 92, 95, 96.

Then identify the number in the middle: 92

Use the data set below to answer question.

90, 92, 96, 95, 92

Use mean to determine the center of the data set.

93

First add all of the data values: 90 + 92 + 96 + 95 + 92= 465.

Then divide the sum by the total number of values:

Use the data set below to answer question.

90, 92, 96, 95, 92

Why are the mean and median different?

Answers may vary

The mean and median differ by one. They are measuring different centers.

The median measures the value that is in the middle. The mean measures the

average value.

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