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## Objective

SWBAT use a frequency distribution to approximate the standard deviation of a large data set.

#### Big Idea

You want me to subtract and square how many numbers?!? Make the process of managing data less crazy using a frequency distribution.

15 minutes

## Put it into Action

30 minutes

Individual Student Work: For this section you will need copies of the Standard Deviation Handout and students will need their data from the previous lesson, "In the Middle".  I have provided a list of places to find large data sets as a resource if you need it.  I tell my students that they will be working independently for this part of the lesson and advise them to use the data sets from yesterday's activity.  If they don't have that data with them, I give them another copy of the height/weight data to work with rather than having them take the time to find their "lost" copy.  I explain that they will be using class intervals for the data and may choose whether to use height or weight or may do both.  If your students don't know how to set class intervals, you may need to review this with the whole class before turning them loose to work on standard deviation.  As my students set up their tables and begin to find the necessary values I walk around offering encouragement and assistance as needed. (MP1, MP4, MP5, MP6) I generally let them use calculators to find differences, squares, sums and square roots, but expect my students to create a table/chart showing the values.  This reinforces the mathematics that generate standard deviation and the connection between simple standard deviation and working with frequency table data.

Class Discussion:  When everyone is done I draw a line down the middle of my front board with one side for height and one for weight.  I then ask my students to post their standard deviation value on the appropriate side.  I have several markers and my students know that they can go up whenever there's an open spot to post, so this process doesn't take very long and allows a certain level of anonymity for students who are less confident about their work.  I then ask my students to review the posted results and pair-share with their left shoulder partner about the differences they see.  I tell them I want them to talk about why there are any differences at all if they were using the same data. (MP2, MP3) After a few minutes (or when the talk dies down) I invite volunteers to share what was discussed with the whole class.  If none of my students mention the fact that they each set their own class intervals as a source of the differences, I ask leading questions to get them there.  For example I might ask "what numbers did you use to find the mean of your data set?" or "How did you determine which values to use for the 'X'?"  I leave the results on the board for the wrap up portion of this lesson and collect the student work for closer review.

## Wrap it Up

10 minutes

I  ask each student to answer the following questions using complete sentences.  Some students may need to turn their responses in at the beginning of class tomorrow in order to do a good job, but I encourage them to try to finish today so I can review their work before the next class.

• Describe the similarities and differences between finding the mean of a data set and the mean of a frequency distribution.
• Describe the similarities and differences between finding the standard deviation of a data set and the standard deviation of a frequency distribution.
• Describe two different examples of when you would use a frequency distribution to estimate mean and standard deviation.

These questions give my students an opportunity to reflect on the mathematical processes (MP2, MP7) they've been working with and give me an idea of what misunderstandings still exist.