# Measuring Variability for Symmetrical Distributions

Videos to help Algebra I students learn how to calculate the standard deviation for a set of data.

Students interpret the standard deviation as a typical distance from the mean.

New York State Common Core Math Module 2, Algebra I, Lesson 5

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Common Core For Algebra I

Lesson 5 Summary

The standard deviation measures a typical deviation from the mean.

To calculate the standard deviation,

1. Find the mean of the data set;
2. Calculate the deviations from the mean;
3. Square the deviations from the mean;
4. Add up the squared deviations;
5. Divide by n - 1 (if you are working with a data from a sample, which is the most common case);
6. Take the square root.

The unit of the standard deviation is always the same as the unit of the original data set.

The larger the standard deviation, the greater the spread (variability) of the data set.

Exercise

How do you measure variability of this data set? One way is by calculating standard deviation.

Jenna has bought a new hybrid car. Each week for a period of seven weeks, she has noted the fuel efficiency (in miles per gallon) of her car. The results are shown below.

45 44 43 44 45 44 43

6. Calculate the standard deviation of these results to the nearest hundredth. Be sure to show your work.

6. Calculate the standard deviation of these results to the nearest hundredth. Be sure to show your work.

Exit Ticket

1. Look at the dot plot below.

a. Estimate the mean of this data set.

b. Remember that the standard deviation measures a typical deviation from the mean. The standard deviation of this data set is either 3.2, 6.2, or 9.2. Which of these values is correct for the standard deviation?

2. Three data sets are shown in the dot plots below.

a. Which data set has the smallest standard deviation of the three? Justify your answer.

b. Which data set has the largest standard deviation of the three? Justify your answer.

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