Not Normal

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SWBAT use sample means to create a normal curve from raw data that is not normally distributed.

Big Idea

Make anything fit the curve! Abnormal can become normal, just apply the Central Limit Theorem using what you learn in this lesson.

Set the Stage

5 minutes

You will want to review the Sample Means Example.doc resource before beginning this lesson and may want to create a copy of the data for an overhead projector or document camera.  This lesson follows a lesson about normal distributions so students are already familiar with the normal curve and using a histogram to check for normalcy.  I introduce this lesson by having a sketch of a normal curve and a sketch of data that is very skewed on the front board.  I listen to the comments my students make as they come into the classroom and use that as a starting point for our class discussion.  For example, if they're talking about the differences between the two graphs and saying one is "normal" and the other isn't, then I don't ask which seems normal, I build on their comments and ask why the second graph is not normal.  I want my students to articulate the criteria for a normal distribution rather than just giving them a list.(MP4, MP7)  When everyone is clear about why the second graph doesn't fit the definition of a normal distribution/normal curve I lament that we won't be able to make good predictions or use the "shortcuts" we've been learning for large data sets...unless there's a way to make the data more normal somehow.  This little bit of drama usually sets my students up to ask if there is some way to do that and how it works, at which point I project the Sample Means example on my front board.  With the Sample Means Example on the board, I explain that by taking samples from a population and creating a frequency table of the means of each sample we can make skewed data become more normal.  Because my students are used to being able to work things out for themselves I'm usually met with skepticism at this statement, so I assure them that they will be able to see how it works in the next activity.

Put it Into Action

35 minutes

You will want to have copies of theNot normal handout.doc and thewage data.xls spreadsheet for this section of the lesson.  I tell my students they will be working with their right shoulder partner for this part of the lesson and give each student a copy of the Not Normal Handout and the Wage data spreadsheet.  I ask them to review the directions with their partners and ask about anything they need clarified.  When everyone is ready I tell them to work carefully and advise them that I will let them know when there are only a few minutes left to finish their graphs. (MP1, MP4, MP6) While they work I walk around offering encouragement and redirecting as needed.  I try to catch mistakes in the making so that my students don't become to frustrated and can make good use of their time.  I generally don't just tell them they're doing something wrong, I ask questions like "How are you making sure your selections are random?" instead of "That's not a random sample."

When all the teams have completed or are almost done with at least three histograms, I tell them they have 5 minutes to finish up.

Wrap it Up

10 minutes