# Data Set in Math: Definition & Examples

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• 0:01 What Is a Data Set?
• 1:01 Mean
• 2:16 Median
• 3:40 Mode
• 4:23 Lesson Summary

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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, learn about data sets and how to use the operations of mean, median, and mode to manipulate the data. Then, test your knowledge with a brief quiz.

## What Is a Data Set?

A data set is a collection of numbers or values that relate to a particular subject. For example, the test scores of each student in a particular class is a data set. The number of fish eaten by each dolphin at an aquarium is a data set.

Data sets can be written as a group of numbers in random order, in a table form or with curly brackets surrounding them. The data sets are usually labeled so you know what the data represents, but when working with data sets, what the data stands for is not always provided and is not always needed to finish the problem.

The three ways to work with data sets are to calculate their mean, median, and mode. But before we can calculate these three pieces of information, we first have to prepare our data set by rewriting them in ascending order from the smallest to the greatest. So, our two data set examples from earlier need to be rewritten as follows:

Now we can go ahead and start working with these data sets.

## Mean

The mean of a data set is its average. To calculate the mean, we add up all our values and divide by the number of items we have.

First, we need to know how many items we have in our data sets. To do this, we count how many values we have. For the test scores, we have 7 items and for the fish eaten we have 8 items.

Second, we need to add up all our values. For the test scores, we add up 64 + 89 + 89 + 92 + 94 + 95 + 100 to get 623. We then divide this number by the number of items this data set has, which is 7. We get 623 / 7 = 89. 89 is our mean for the test scores data set. For the fish eaten data set, we do the same thing. We add 8 + 10 + 10 + 10 + 12 + 15 + 18 + 20 = 103 and divide by the number of items to get 103 / 8 = 12.875. So, 12.875 is our mean for the fish eaten.

## Median

The median is the middle value of our data set. It is the number in the exact middle of our data set when it is written in ascending order. Calculating the median is different for data sets with an odd or even number of items.

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