Learning Goals
In this support activity you’ll become familiar with the following:
You will also have an opportunity to refresh the following skills:
This support activity will give you more practice calculating mean and median and how to interpret comparisons of mean and median.
In Calculating Mean and Median of a Data Set: What to Know, you had a chance to calculate the mean and median of a small data set by hand. As you work through this activity, return to that section as needed to refresh the formula and the process.
Recall
Before you begin, recall the definitions of mean and median.
Core skill:
Core skill:
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] |
question 1
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.
Recall
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 that information here if needed.
Core skill:
question 2
Let’s use technology to verify the result you obtained for the median in Question 2.
Go to the Describing and Exploring Quantitative Variables tool at https://dcmathpathways.shinyapps.io/EDA_quantitative/ and confirm your answer using the online 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 $)”.
Step 5) 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.
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 50th percentile.
