What does standard deviation measure in a data set?

The spread or variation of the data points around the mean.

Describe the relationship between a normal distribution curve and standard deviation. How does the shape of the curve change with a larger or smaller standard deviation?

In a normal distribution, the standard deviation determines the width of the bell-shaped curve. A larger standard deviation results in a wider, flatter curve, indicating greater variability in the data. A smaller standard deviation results in a narrower, taller curve, indicating less variability and data points clustered closer to the mean.

A researcher measures the heights of a sample of plants and calculates a standard deviation of 2 cm. Explain what this standard deviation indicates about the variability in the heights of the plants.

A standard deviation of 2 cm indicates that the heights of the plants in the sample typically vary by about 2 cm from the average height. This provides a measure of how much the individual plant heights differ from the mean height of the sample.

Calculating Standard Deviation

12th GradeMath20 min

Learning Objective

I can calculate standard deviation to analyze data sets.

Lesson Flow

Watch Video

8 min

Standard Deviation

Bozeman Science

Guided Notes

5 min

Key concepts students will learn:

•
Standard deviation measures the spread or variation in a data set, often visualized as a bell-shaped curve called a normal distribution.
•
Approximately 68% of data points fall within one standard deviation from the mean, while 95% fall within two standard deviations.
•
The formula for standard deviation involves calculating the square root of the variance, which is the average of the squared differences from the mean.

Practice

10 min

3 questions • Multiple choice & Short answer

Exit Ticket

5 min

“Calculate the standard deviation of the following data set: 2, 4, 6, 8, 10. Show all steps.”

Teacher Guide

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Answer keys for all questions
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Calculating Standard Deviation

Learning Objective

Lesson Flow

Watch Video

Guided Notes

Practice

Exit Ticket

Teacher Guide

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