- Name and compare the measures of center shown in a graph
Calculating Mean and Median using Technology
Calculating mean and median by hand is straightforward when we have a small data set. However, when computing these values with a large data set, it is not so efficient to do by hand. Instead, we will rely on technology to calculate these values.
Let’s try now with the Sleep Study data set. This data set contains the average number of hours of sleep per night for each of the [latex]253[/latex] students in the sleep study. Go to the statistics technology tool below:
STEP 1: Select the “Single Group” tab.
STEP 2: Locate the dropdown under “Enter Data” and select “From Textbook.”
STEP 3: Locate the drop-down menu under “Data Set” and select “Sleep Study: Average Sleep.”
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Note the Descriptive Statistics located above the graphical display in the tool. You’ll find the mean and median located in the list. Eventually, we will use all the values shown but, for now, we just want to record the mean and median. To use the tool to calculate descriptive statistics for any data set, load, copy and paste, or type the data values into the “Observations” box of the tool, and it will automatically list the values in the “Descriptive Statistics.”
“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.
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 the exercises above). Go to the statistics technology tool:
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 the Try It question below (Note: the mean and median will be automatically calculated by the technology and can be found under Descriptive Statistics).
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Recall that we consider the mean to be 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.