Understand and be able to calculate the standard deviation for a set of data.

Materials

Data set

Calculator

Plotting paper

Pen or pencil

Warm-up

Ask students if they have heard of the term standard deviation before and what it means. Allow a few students to answer and discuss their answers.

Direct Instruction

Introduce the concept of standard deviation as a measure of variability or how spread out data is. Explain that it tells us how far data points are from the mean, and how much data is spread out from the mean.

Using the data set from the warm-up, calculate the standard deviation for the data set.

Using the data set from the warm-up, calculate the mean for the data set.

Using the data set from the warm-up, plot the data points on a graph and draw a line to approximate the mean.

Using the data set from the warm-up, calculate the standard deviation for the data set.

Using the data set from the warm-up, calculate the mean for the data set.

Using the data set from the warm-up, plot the data points on a graph and draw a line to approximate the mean.

Compare the standard deviation and the mean for the two data sets. Ask students to describe what they notice about the differences between the two standard deviations and mean.

Discuss the importance of standard deviation in statistics and how it is used in real-world situations.

Guided Practice

Divide students into small groups and give each group a different data set.

Have students calculate the standard deviation and the mean for their data set.

Have students plot their data points on a graph and draw a line to approximate the mean.

Have them compare their standard deviation and mean to the previously calculated values.

Have students discuss what they notice about the differences between their standard deviation and mean and the previously calculated values.

**Hint: **Some groups may have a lower standard deviation than the mean, while others may have a higher standard deviation than the mean.

Independent Practice

Have students work individually or in pairs to calculate the standard deviation and the mean for a new data set.

Have them plot the data points on a graph and draw a line to approximate the mean.

Have them calculate the standard deviation and the mean for the data set a second time.

Have them compare their two calculations of the standard deviation and the mean.

Have students discuss what they notice about the differences between their two calculations of the standard deviation and the mean.

Have students use their calculators to calculate the standard deviation and the mean for a third data set.

Have them plot the data points on a graph and draw a line to approximate the mean.

Have them calculate the standard deviation and the mean for the data set a second time.

Have them compare their two calculations of the standard deviation and the mean.

Have students discuss what they notice about the differences between their two calculations of the standard deviation and the mean.

Closure

Review the concept of the standard deviation and its importance in describing data sets.

Discuss the importance of being able to calculate the standard deviation.

Ask students to share their thoughts on the differences between their two calculations of the standard deviation and the mean.

Ask students to share any challenges they faced when calculating the standard deviation and the mean for the different data sets.

Ask students to share any insights they gained from comparing their two calculations of the standard deviation and the mean.

Assessment

To assess student understanding, have students complete a short quiz or worksheet on the concept of the standard deviation and its calculation. This could include questions on the concept of the standard deviation and its importance in statistics, as well as multiple-choice questions on calculating the standard deviation and the mean for a data set.

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