What you’ll need to know
In this support activity you’ll become familiar with the following:
You will also have an opportunity to refresh the following skills:
In the next section of the course material and in the following activity, you will need to compare the mean and median of a quantitative variable and calculate mean and median by hand and using technology. This support activity will give you more practice calculating mean and median and will set the stage for interpreting the comparisons of mean and median in the upcoming section.
In What to Know About Calculating Mean and Median of a Dataset: 4A, you had a chance to calculate the mean and median of a small dataset by hand. As you work through this activity, return to that section as needed to refresh the formula and the process.
Before you begin, recall the definitions of mean and median.
Core skill:
Core skill:
Salaries
In this activity, we’ll be using the two datasets listed below. Suppose that the first dataset lists the monthly salaries (in thousands of dollars) for all six employees at a company during the month of January.
| Employee |
Monthly Salary in January (in thousands of dollars) |
| Employee 1 | 4 |
| Employee 2 | 6 |
| Employee 3 | 3 |
| Employee 4 | 5 |
| Employee 5 | 6 |
| Employee 6 | 3 |
Then, suppose that one of the employees gets a large raise in February. The second dataset lists the monthly salaries (in thousands of dollars) for the same six employees during the month of February.
| Employee |
Monthly Salary in February (in thousands of dollars) |
| Employee 1 | 4 |
| Employee 2 | 8 |
| Employee 3 | 3 |
| Employee 4 | 5 |
| Employee 5 | 6 |
| Employee 6 | 3 |
question 1
Compare and contrast the two datasets: how are they similar and how are they different?
Now consider just the dataset of employee salaries from January. We’d like to know the median salary for the six employees for the month of January.
Calculate the median of a dataset by hand
Recall
To answer the question below, you’ll need to calculate the median of a dataset containing an even number of values. You can refresh that information here if needed.
Core skill:
question 2
By hand or with a regular calculator (without using the median function), calculate the median employee salary in January (in dollars).
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? Consider now, what the median implies about the data.
question 3
What does the median tell you about the salaries of the employees in January?
Calculate the mean of a dataset by hand
question 4
By hand or with a regular calculator (without using the mean function), calculate the mean employee salary in January (in dollars).
question 5
Confirm your answer using the online tool.
question 6
What does the mean tell you about the salaries of the employees in January?
question 7
The median and mean employee salaries for January are the same. Why is this?
Compare the mean and median of different datasets
Now consider the dataset of employee salaries from February. First we’ll calculate the median of this set, then consider how we might expect the mean of the February salaries compares to the mean of the January salaries.
question 8
What is the median employee salary in February (in dollars)? You may use either the online tool or calculate by hand.
question 9
Without calculating the mean employee salary in February, what do you predict will be true about the February mean compared to the January mean and why?
question 10
Now, calculate the mean employee salary in February (in dollars). You may use either the online tool or calculate by hand.
Now consider a slightly different question.
question 11
Suppose that in March, Employee 6 quits and the company takes on an unpaid intern. How will the median and mean change from February to March?
It may take some time before you really feel comfortable interpreting means and medians and understanding what they imply about a dataset. A key idea to take from this activity is that, while the median stays relatively fixed in a dataset if one value changes by a large amount, the mean does not. This tells us that the mean is sensitive to the presence of extreme values in the dataset.
It’s okay if you need more practice to process the sensitivity of the mean. But if you feel comfortable calculating the means and medians in this activity by hand and using technology, please move on to the next section and activity.
