The mathematical purpose of the lesson is for students to recognize outliers, to investigate their source, to make decisions about excluding them from the data set, and to understand how the presence of outliers impacts measures of center and measures of variability. This lesson relies on work in previous lessons in which students found measures of center and variability. This lesson connects to upcoming work because students will investigate outliers when dealing with bivariate data in another unit. Students encounter the term outlier which is a data value that is unusual in that it differs quite a bit from the other values in the data set.
When students have to analyze data in the context of a problem to determine whether or not to exclude an outlier, they are reasoning abstractly and quantitatively (MP2). This reasoning process is also an aspect of mathematical modeling (MP4).
- Describe (orally and in writing) how outliers impact measure of center and measures of variability.
- Determine (in writing) when values are considered outliers, investigate their source, and determine if they should be excluded from the data.
- Let’s investigate outliers and how to deal with them.
Acquire devices that can run GeoGebra (recommended) or other spreadsheet and statistical technology. It is ideal if each student has their own device. (A GeoGebra Spreadsheet is available under Math Tools.)
- I can find values that are outliers, investigate their source, and figure out what to do with them.
- I can tell how an outlier will impact mean, median, IQR, or standard deviation.
A data value that is unusual in that it differs quite a bit from the other values in the data set. In the box plot shown, the minimum, 0, and the maximum, 44, are both outliers.
A measure of the variability, or spread, of a distribution, calculated by a method similar to the method for calculating the MAD (mean absolute deviation). The exact method is studied in more advanced courses.
A quantity that is calculated from sample data, such as mean, median, or MAD (mean absolute deviation).