# Lesson 12

Standard Deviation

### Lesson Narrative

The mathematical purpose of this lesson is to introduce standard deviation and understand that it is a measure of variability. Previously, students understood the meaning of MAD and IQR; standard deviation fits into their understanding as another measure of variability. Future lessons build on this lesson when students interpret standard deviation in context. Standard deviation is a measure of variability calculated by:

• Finding the square of the distance from the mean to each value.
• Then finding the sum of these square distances and dividing by n (the number of values in the data set).
• Finally, finding the square root of this sum.

When students manipulate data to achieve various specified measures of center or variability they are engaging in MP2 because they have to make use of the structure underlying standard deviation as a measure of variability.

Note that in this unit, all standard deviations refer to the population standard deviation ($$\sigma$$) calculation rather than the sample standard deviation ($$s$$).

### Learning Goals

Teacher Facing

• Comprehend (in spoken and written language) standard deviation as a measure of variability.
• Use technology to compute standard deviation.

### Student Facing

• Let’s learn about standard deviation, another measure of variability.

### Required Preparation

Acquire devices that can run GeoGebra (recommended) or other spreadsheet technology. It is ideal if each student has their own device. (A GeoGebra Spreadsheet is available under Math Tools.)

Students should have access to technology for calculating standard deviation and mean. Optional activities require technology for creating dot plots and calculating standard deviation, mean, and IQR.

### Student Facing

• I can describe standard deviation as a measure of variability.
• I can use technology to compute standard deviation.

Building On

### Glossary Entries

• standard deviation

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.

• statistic

A quantity that is calculated from sample data, such as mean, median, or MAD (mean absolute deviation).

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