Wiki Page, Math 13 - Perez Sandbox : Module 6 - Wrap Up "Measures of Spread about the Median"

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2026-01-17T21:15:52-08:00

Let’s Summarize

The five-number summary of a distribution consists of the minimum, quartile 1, median, quartile 3, and maximum.

The IQR is the measure of spread we should use when using the median to measure center. It is the distance from Q1 to Q3 and tells us how much variability there is in the middle half of the data.

We can use the median (Q2) to represent the center of a distribution. If we want to summarize the distribution with one number, we can use the median. If we want to summarize the distribution with an interval of numbers, we can use the interval Q1 to Q3, which is the start and end of the middle half of the distribution.

We can use the 1.5*IQR Rule to identify outliers. Outliers are data values that are:

More than 1.5 IQRs greater than Q3 (i.e., the value is greater than Q3 + 1.5 * IQR), or

More than 1.5 IQRs less than Q1 (i.e., the value is less than Q1 - 1.5 * IQR).

The boxplot is a graphical representation of a data set. It displays the five-number summary and highlights any points that are considered outliers (using the 1.5 * IQR rule described in the previous bullet).

Side-by-side boxplots are commonly used to compare two data sets.

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