Describing Data Numerically: Background You’ll Need 3

  • Calculate the median of a data set by hand

This support activity will give you more practice calculating mean and median, including how to interpret comparisons of mean and median.

Before you begin, recall the definitions of mean and median.

In this activity, we’ll be using the two data sets listed below.

Suppose that the first data set lists the monthly salaries (in thousands of dollars) for all six employees at a company during the month of January. For example, Employee [latex]1[/latex] made [latex]\$4,000[/latex] in salary in January. Employee [latex]2[/latex] made [latex]\$6,000[/latex], and so on. We’ll consider this amount the regular salary per month for each of these employees.

The second data set lists the monthly salaries (in thousands of dollars) for the same six employees during the month of February.

Can you locate which employee got the raise?

Employee

Monthly Salary in January

(in thousands of dollars)

Monthly Salary in February

(in thousands of dollars)
Employee 1 [latex]4[/latex] [latex]4[/latex]
Employee 2 [latex]6[/latex] [latex]8[/latex]
Employee 3 [latex]3[/latex] [latex]3[/latex]
Employee 4 [latex]5[/latex] [latex]5[/latex]
Employee 5 [latex]6[/latex] [latex]6[/latex]
Employee 6 [latex]3[/latex] [latex]3[/latex]

Calculating Median

Now, let’s look at the first data set only: The monthly salaries (in thousands of dollars) for all six employees at a company during the month of January.

To answer the question below, you’ll need to calculate the median of a data set containing an even number of values. You can refresh yourself on that information here if needed.

Let’s use technology to verify the result you obtained for the median above.

Go to the Describing and Exploring Quantitative Variables tool below and confirm your answer using the statistical tool.

Step 1: Select the Single Group tab.

Step 2: Locate the drop-down menu under Enter Data and select Your Own.

Step 3: Under Do you have, select Individual Observations.

Step 4: Under Name of Variable, type “January Salaries (in thousands $).”

Under Enter observations, enter the data list, separated by spaces: “4 6 3 5 6 3.” The median will be among the Descriptive Statistics listed in the tool.

[Trouble viewing? Click to open in a new tab.]

How did you do? Did your calculation match the one in the tool? Now, consider what the median implies about the data. Remember that we think of the median as the [latex]50^{th}[/latex] percentile.

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