Summary of Calculating the Mean and Median of a Data Set

Monitoring Your Readiness

To effectively plan and use your time wisely, it helps to think about what you know and do not know. For each of the following, rate how confident you are that you can successfully do that skill. Use the following descriptions to rate yourself:

5—I am extremely confident I can do this task.

4—I am somewhat confident I can do this task.

3—I am not sure how confident I am.

2—I am not very confident I can do this task.

1—I am definitely not confident I can do this task.

Skills Needed for Calculating Mean and Median of a Data Set: Forming Connections

Skill or Concept: I can . . . Questions to check your understanding Rating from 1 to 5
Calculate the mean and median of a data set by hand, as well as with technology. 1, 2
Calculate the mean and median for multiple groups using technology. 5, 6, 7
Estimate the mean and median by looking at the data presented in a histogram. 3, 4

Now use the ratings to get ready for your next in-class activity. If your rating is a 3 or below, you should get help with the material before class. Remember, your instructor is going to assume that you are confident with the material and will not take class time to answer questions about it.

Ways to get help:

  • See your instructor before class for help.
  • Ask your instructor for on-campus resources.
  • Set up a study group with classmates so you can help each other.
  • Work with a tutor.

Essential Concepts

  • The mean of a data set can be computed by summing the data values and dividing by the number of values.
  • The median of a data set can be computed by ordering the data values and identifying the value in “the middle”.
  • The mean represents the balance point of the data, and the median represents the 50th percentile, or the value that splits the data in half.

Study Tips: Evidence-based strategies for learning

  • Create a mnemonic to remember the difference between mean and median. For example,
    • meAn = Average
    • meDian = miDdle
  • Explain how to identify the mean to a friend, real or imaginary, using precise and concise language, then paraphrase. Do the same for the median. For example,
    • To find the mean, divide the sum of the data values by the total number of them. It represents what each value would be if the total were distributed equally across each of them.
    • To find the median, locate the middle-most value of an ordered list of values. If there are an odd number of values, the middle one will be the one in the very middle. If there are an even number of values, the middle value will be the mean of the middle two.
  • To test your understanding of the way mean and median are used as measures of the center of data, and how to use a histogram to answer questions about the center of a distribution, read the What to Know text and questions, pausing to write precise and concise notes from memory.

Foundational Knowledge

Key Equations

  • Mean

[latex]\dfrac{\text{sum of data values}}{\text{total number of data values}}[/latex]               or              [latex]\bar{x}=\dfrac{\sum{x}}{n}[/latex]

where [latex]\bar{x}[/latex] is the mean, [latex]{\sum{x}}[/latex] is the symbol for “sum of”, [latex]{x}[/latex] represents the data values, and [latex]{n}[/latex] is the total number of data values.

Glossary

mean
an average of a set of values calculated by adding the values and then dividing the total by the number of values in the data set.
median
the “middlemost” value of a set of values listed in numerical order.

 

My Skills Checklist:

  • I can use the mean and median as numerical measures to represent the “center” of quantitative data.
  • I can calculate the mean and median with technology to make comparisons between groups.
  • I can make connections between the measures of center and graphical representations of data (e.g., histogram).

Check mark list on clipboard

Topic Complete – now test your understanding in the Self-Check.