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.
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.
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.
Over 79,000 lessons in all major subjects
Get access risk-free for 30 days,
just create an account.
If the data set has an odd number of items, we find the middle value and that is our median. The test scores data set has an odd number of items which are 64, 89, 89, 92, 94, 95, and 100, so our median is the middle value, or the fourth term in the sequence, which is 92. Notice how the fourth term has the same number of terms before and after it? It is the middle term in the data set.
If the data set has an even number of items, though, we need to find the two middle values and get their average. The fish eaten data set, for example, has an even number of items. So we need to find the two middle values from 8, 10, 10, 10, 12, 15, 18, and 20, which are 10 and 12. These are the fourth and fifth terms, respectively. If you notice, these two terms have the same number of terms before and after them. They are in the middle. Our median, then, for the fish eaten data set is the average of 10 and 12, which is (10 + 12) / 2 = 22 / 2 = 11.
The mode of a data set is the number or value that occurs most often in the data set. It is possible to have more than one mode in a data set, and it is also possible to have no modes in a data set. Looking at our test scores data set 64, 89, 89, 92, 94, 95, and 100, we see that the number 89 occurs most frequently. All the other values are not repeated. So our mode for the test scores data set is 89. The fish eaten data set of 8, 10, 10, 10, 12, 15, 18, and 20 has a mode of 10 because that number occurs three times while all the other numbers occur just once.
Let's review. Data sets are a collection of numbers related by a topic. The three ways to work with data sets include mean, median, and mode. The mean is the average of the data set, the median is the middle of the data set, and the mode is the number or value that occurs most often in the data set. Before working with data sets, we must write them in ascending order.
Did you know… We have over 200 college
courses that prepare you to earn
credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the
first two years of college and save thousands off your degree. Anyone can earn
credit-by-exam regardless of age or education level.