# In the Middle

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## Objective

SWBAT find the mean of a frequency distribution, assuming a normal distribution.

#### Big Idea

Too much data! Too many numbers! Use a frequency distribution to find the mean.

## Set the Stage

10 minutes

You will want to have a copy of a very large data set ready to show your students for this section of the lesson.  This should be the same data they will be working with in the Put it into Action section, but you may want to have additional data sets as well, to emphasize large data sets.  I begin class with the following question on the board, "Describe three measures of center".  As my students come into the room I listen to their discussions and can quickly gauge how much time I'll need to spend setting up today's lesson.  After the bell, I ask for a volunteer to write the measures on the board.  I allow them to "use a lifeline" if necessary, but generally this is review and my students do fairly well with it.  Since we'll be working with some new concepts later, I like to begin with something reassuring for them.  When the words "mean, median, mode" are posted, I ask my students to pair share what each word means, mathematically.  I then call on random teams to share their discussion with the class.    When we're all clear on these terms, I ask my students which one is the best representation of the center of a data set.  This is a bit tougher because there are circumstances for which each is better than the others.  I allow the discussion to go for a bit, asking leading questions until my students recognize that if the data set is unimodal without outliers or much skewness, the mean works best.  Again, this should be review, so it doesn't take very long and is a good opportunity to set things up for the rest of the lesson.  Once we establish that we'll be working with the mean, I write a short set of numbers on the board and ask them to find the mean individually without their calculators (or cell phones!)  I use a simple set like (5,5,8,10) and ask for a volunteer to work the problem on the board.  There are usually several willing students and we quickly finish our review by following as the volunteer adds the four numbers to get 28 then divides by n=4 to get the answer of 7.  To finish this section of the lesson, I project the Height Weight Data set on my whiteboard and challenge my students to again find the mean, telling them they can work with either height or weight.  Amid the chorus of groans that ensue there is almost always some student who asks to use the calculator. (MP5)  I turn off the projection and assure them that we will eventually be using both calculators and computer software like Excel, but that for today's lesson I'm going to show them another way to estimate the mean that goes much more quickly.

40 minutes

## Wrap it Up

5 minutes

I allow students who need additional time to write their responses to the handout to turn in their work at the beginning of class tomorrow and otherwise collect the assignment at the end of class. When all teams have completed the activity including their written responses to the questions on the handout, I ask them to pair-share the following discussion questions:

• What part of this activity was most difficult and why?
• What part of this activity was easiest and why?
• Would you have preferred to find the mean of this data (by hand) without using a frequency table and why?

I have my students do this closure piece both so that they have a structured opportunity to reflect and so that I can listen for persistent misconceptions or concerns as I walk around.