What is the Center in a Data Set? - Definition & Options

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  • 0:04 Finding Your Center
  • 0:43 Using Mean
  • 1:34 Using Median
  • 3:52 Lesson Summary
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Finding the center in a data set can sometimes be a little confusing. This lesson will help you determine the correct method for finding the center in a data set, and when you are finished, test your knowledge with a short quiz!

Finding Your Center

Elizabeth is working on a science project. She is testing the effectiveness of bleach on certain types of stains. After trying the bleach on each stain five times, Elizabeth records how many times the bleach removes the stain completely. Check out this chart to see how the project turned out.

Data representing how many washes it takes to remove a stain with bleach
data chart

Elizabeth has a data set of 4, 2, 5, 4, 1, 2 and 3. She wants to find a way to summarize the information. Elizabeth needs to find the center of data, a single number that summarizes the entire data set. You can find the center of data using either the mean or the median of the data set.

Using Mean

The mean is the sum of the numbers in a data set divided by the total number of values in the data set. The mean is also commonly known as the average. The mean can be used to get an overall idea or big picture of the data set. Mean is best used for a data set with numbers that are closer together.

Since all of Elizabeth's numbers are close together, she can use mean to find the center of her data set. Simply add all of the numbers together and divide by how many numbers there are in the data set: 4 + 2 + 5 + 4 + 1 + 2 + 3 = 21 / 7 = 3. Elizabeth's center of data for this data set is 3. She can summarize that, on average, bleach will effectively remove a stain 3 out of 5 times.

Using Median

Elizabeth is now experimenting with the effectiveness of plain soap on stains. After trying the soap on stains eight times, Elizabeth records how many times the soap removes the stain completely. Check out the chart she has made showing the effectiveness of soap on the stains.

Data representing how many washes it takes to remove a stain with soap
data chart

From this chart you can see that our data set is 6, 7, 8, 8, 6, 0 and 7. You might notice that we have several numbers that are close together and one number that is a bit off. This number is referred to as the outlier. An outlier is a value that is much larger or smaller than the other values in a data set, or a value that lies outside the given data set. Because we have an outlier in this data set, we need to use the median to find the center of the data set.

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