Lesson 7 Bridging the Gap Solidify Understanding

Learning Focus

Understand standard deviation.

How does standard deviation compare to range as a measure of spread?

Technology guidance for today’s lesson:

Calculate the Standard Deviation for a Data Set: Casio ClassPad Casio fx-9750GIII

Open Up the Math: Launch, Explore, Discuss

Your job in this task is to figure out what the standard deviation measures are and to get a sense of how changes in data affect standard deviation. Your teacher will give you a set of strips that each contain a set of data and a dot plot that represents the data. Follow the instructions for each problem below, and be prepared to discuss your findings.

1.

a.

Use technology to find the standard deviation for each set of data on the strips you have been given.

b.

Arrange the strips with the standard deviations from least to greatest. Write the sets they represent here. Describe any patterns or trends that you notice.

2.

Compare data sets 4 and 2. Which one has the greater standard deviation? Why do you think the standard deviation is greater for this data set?

3.

Look at data set 6. What impact did the $10$ have on the standard deviation? What would happen to the standard deviation if you eliminated this data point? What would happen if you made the $10$ a greater number?

4.

Compare data sets 6 and 7. What do you notice about the standard deviations for these data sets? Why do you think this is the case?

5.

Create your own set of data that has exactly the same standard deviation as data set 2 but a different mean.

6.

What does the standard deviation help describe in a distribution?

7.

Samantha is entering a bridge-building contest for her math class. The winner of the contest will be the student who can build the bridge that holds the most weight. As she is getting ready to build her bridge, she has narrowed her decision down to three different designs that she could use for her bridge. She has data from bridges that have used the three different bridge designs from previous years, and she is trying to decide which design to go with. The data for the amount of weight, in pounds, for the three different types of designs are given below. Which bridge design should she use? Use both graphs and numerical summaries to back up your decision for the best design.

Design #1: $850$ , $912$ , $980$ , $1012$ , $1060$ , $1407$ , $1600$ , $1602$ , $1680$ , $1700$

Design #2: $1380$ , $1390$ , $1402$ , $1425$ , $1450$ , $1455$ , $1477$ , $1490$ , $1493$ , $1500$

Design #3: $650$ , $740$ , $807$ , $890$ , $906$ , $920$ , $925$ , $960$ , $980$ , $1003$ , $2257$

Ready for More?

Explain why outliers affect the standard deviation. Do outliers make the standard deviation less or greater?

Takeaways

Standard deviation:

Standard deviation and mean:

Vocabulary

standard deviation
Bold terms are new in this lesson.

Lesson Summary

In this lesson, we learned about standard deviation, a measure of spread for single-variable quantitative data. The standard deviation is $0$ when all the data have the same value.

Retrieval

Students were surveyed about how they prefer to use their free time and what they like to eat. They were asked if they prefer listening to music or watching videos. They were also asked if they prefer side dishes or salads. Use the data from the survey in the table to answer the questions.

	Listening to Music	Watching Videos
Side Dishes	$48$	$97$
Salads	$32$	$53$

1.

How many students were surveyed?

2.

How many students prefer watching videos?

3.

Out of those who prefer listening to music, what percent like side dishes?

4.

Use the zeros and the graph to write the equation of the quadratic function in factored form.