Instructor Guide Calculating the Mean and Median of a Dataset: Forming Connections

Overview

  • This in-class activity introduces the concepts of mean and median as measures of center for numerical data.
  • Students will use technology to calculate measures of center, compare groups using the mean and median, and build connections between measures of center and graphical representations of numerical data (e.g., histogram).
  • This activity connects back to Visualizing Quantitative Data, Applications of Histograms, and Comparing Quantitative Distributions, and prepares students for Interpreting the Mean and Median of a Dataset.
  • [a list of tags like S2, O1, B1, V3] ← Link to EBTP descriptions 

Prerequisite assumptions

Students should be able to do each of the following after completing the What to Know assignment.

  • Calculate the mean and median of a small data set by hand.
  • Use a data analysis tool to calculate the mean and median of a large data set.
  • Estimate the mean and median of a data set by examining a histogram of its distribution.
  • Use a data analysis tool to calculate and compare the mean and median for multiple groups at once.
  • Use a histogram to estimate and compare centers for multiple groups.

Intended goals for this activity

After completing this activity, students should understand that the mean and median are numerical measures used to represent the “center” of quantitative data. They should be able to calculate the mean and median with technology to make comparisons between groups and make connections between the measures of center and graphical representations of data (e.g., histogram).

Synchronous Delivery and Activity Flow

The sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.

Frame the activity (3 minutes)

  • This class will rely heavily on the Data Analysis Tool. Ensure each group or pair has access to the tool.
  • Ask Question 1 and allow students some time to reflect and share.
  • Point out that one of the variables that will be the focus of the activity, Poor Sleep Quality Score, is given as a numerical value telling us about the individual’s quality of sleep; a larger score indicates a worse quality of sleep.

Activity Flow (18 minutes)

  • Have students work in pairs or groups to address Question 2 before reconvening as a class to discuss what they found and to address any concerns.
  • Students will continue in pairs or groups to complete the activity.
  • Students may struggle to estimate the values in question 6 since the means are relatively close for each of the groups. Encourage them to communicate exactly why they feel estimating the values is a challenge. What is it about the distributions (e.g., shape, spread) that makes it so challenging to estimate the mean?

Wrap-up/transition (5 minutes)

  • At the end of the activity, ask students to reflect back to their responses to the open-ended question at the beginning of the activity. Were they surprised at what they discovered from the data?
  • Prompt students to reflect on the use of histograms in the activity: “Do you think it is possible to look at a histogram and guess whether the mean or median might be larger? If so, what characteristics or features of a histogram might suggest that the mean is larger? What characteristics or features of a histogram might suggest that the median is larger?”
  • Have students refer back to the Objectives for the activity and identify ones they recognized completing. S2, C4, O2
  • Assign the homework or Practice and any What to Know pages for the Forming Connections activities you plan to complete in the next class meeting. C2