Key Concepts

• If a distribution is perfectly symmetrical, the mean and median are the same.
• If a distribution is skewed, the mean and median are not the same.
• If a distribution has more data on the left and less on the right, it is skewed to the right and the mean is larger than the median.
• If a distribution has more data on the right and less on the left, it is skewed to the left and the mean is smaller than the median.

Glossary

mean: a number that measures the central tendency of the data; a common name for mean is “average.” The sample mean is written as [latex]\overline{x}[/latex] and the population mean is written as [latex]\mu[/latex].

median: a number that separates ordered data into halves; half the values are the same number or smaller than the median, and half the values are the same number or larger than the median. The median may or may not be part of the data.

mode: the value that appears most frequently in a set of data

symmetrical: a distribution is symmetrical if a vertical line can be drawn at some point in the histogram such that the shape to the left and the right of the vertical line are mirror images of each other.

skewed: used to describe data that is not symmetrical. When the right side of a graph looks “chopped off” compared to the left side, we say it is “skewed to the left.” When the left side of the graph looks “chopped off” compared to the right side, we say the data is “skewed to the right.” Alternatively, when the lower values of the data are more spread out, we say the data are skewed to the left. When the greater values are more spread out, the data are skewed to the right.