Overview
This lecture explains how to calculate and interpret the median, especially for even-sized data sets, and when to use the median versus the mean as a measure of center.
Calculating the Median (Even Number of Values)
- Arrange the data in order from smallest to largest before finding the median.
- If the number of data values is even, find the two middle values.
- Calculate the median by averaging the two middle values (add them and divide by two).
- Example: For values 19, 20, 24, 27, 28, 30, the median is (24 + 27) ÷ 2 = 25.5.
Using a Calculator for Median
- Enter data into List 1 on your graphing calculator.
- Use the "1-VarStat" function to calculate mean, standard deviation, and median.
- Scroll down in the "1-VarStat" results to find the median, labeled "Med."
Interpreting Mean and Median
- Both mean and median represent the center or "typical" value of a data set.
- The interpretation templates for mean and median are the same; both describe the typical value.
Deciding Between Mean and Median
- Use the mean when the data's histogram is symmetric.
- Use the median when the data's histogram is skewed.
- Identifying the shape of the data is the first step in choosing the correct measure of center.
Example: Skewed Data Set
- Given skewed CO2 emission data, the shape of the histogram is skewed.
- For skewed data, use the median to describe the typical value.
Key Terms & Definitions
- Median — The middle value in an ordered data set; if even, the average of the two middle values.
- Mean — The average of all values in a data set.
- Skewed — A distribution where data is not symmetrically distributed; one tail is longer.
- "1-VarStat" — Calculator function that computes mean, median, and standard deviation for a data set.
Action Items / Next Steps
- Practice calculating and interpreting the median for both symmetric and skewed data sets.
- Use your calculator's "1-VarStat" function to find mean and median.
- Complete any assigned homework on measures of center and interpreting data distributions.