Mean and Median as the Center of Data
There are other ways that we can think about the mean and median as measures of center of numerical data. More specifically, the mean represents the balance point of the data, and the median represents the [latex]50[/latex]th percentile, or the value that splits the data in half (i.e., half of the data are below the median and the other half of the data are above the median).
mean and median
[Perspective Video – a 3-instructor video illustrating the mean as a balance point and the median as splitting the data in half]
question 3
question 4
Using Technology to Calculate and Compare Centers Across Groups
[Worked example video – a 3-instructor video providing an example like the one below for questions 5 – 7]
Another benefit of using technology to calculate the mean and median is that we can quickly calculate these values for multiple groups. We can do so by using the Several Groups tab on the Describing and Exploring Quantitative Variables tool (the same tool you used to complete questions 2 – 4 above).
Go to the Describing and Exploring Quantitative Variables tool at https://dcmathpathways.shinyapps.io/EDA_quantitative/.
Step 1) Select the Several Groups tab.
Step 2) Under Enter Data, select From Textbook.
Step 3) Locate the drop-down menu under Data Set, and select Sleep Study: Average Sleep Score.
Step 4) Change Choose Type of Plot to Histogram if desired.
Step 5) Calculate the mean and median for each of the groups: “Owl,” “Lark,” and “Neither,” and list these values in the table in question 5 below (Note: the mean and median will be automatically calculated by the technology and can be found under Descriptive Statistics).
Recall that “Owl” describes the group of students who tends to stay up late, and “Lark” describes the group who tends to wake up early. Students who did not identify as an owl nor a lark were classified in the “Neither” group.
Recall also that we consider the mean to be the arithmetic mean (commonly called the “average”) of a set of numbers, while the median refers to the value that sits in the middle of the distribution with half of the values above it and half of the values below.
