Measures of Central Location
The Median
Learning Outcomes
Understand and calculate medians both by hand and in Excel.
- The value of the middle number
- Or the mean of the two middle numbers when there are an even number of data
- To calculate: order the numbers from smallest to largest then find the middle number or average of two middle numbers (for even sized data sets)
Knowledge Check 2.1 – Finding the Median
Step 1:
Step 2:
Conclusion: The median value of the data set is 23.
Example 2.2
Find the median of the following numbers: 25, 19, 24, 23, 28, 21
Step 1: Order the data: 19, 21, 23, 24, 25, 28
Step 2: Find the middle values: 19, 21, 23, 24, 25, 28
Step 3: Average the middle values: (23 + 24)/ 2 = 23.5
Conclusion: The middle value (median) for the above data set is 23.5.
Example 2.3.1
Find the median using Excel.
- We use the =median() call in Excel to calculate the median.
- See the video below.
- Click here to download the solution shown in the video below.
Example 2.3.2
- The mean can be greatly affected by outliers (extreme values)
- The median is a better reflection of the middle value in data set because it does not get affected by extreme values
- See the video below for an example.
- Click here to download the Excel file shown in the video below.
Key Takeaways: The Median
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