Type of activity: In-class, large-group

Statistical topics: histograms, location, variability, and shape of distributions

Time needed:  15 minutes, or more depending on the amount of discussion generated

Materials needed:

• A large lecture hall with fixed seating, such as 101 or 102 Thomas Building, with at least 15 rows
• At least 30 female students and at least 30 male students

1. Ask the students to vacate all of the classroom seats.  In doing so, ask the females to stand in the front-right corner of the classroom, and ask the males to stand in the rear-left corner of the classroom.  (Students tend to want to take their belongings with them.  To save time and prevent chaos, I try to encourage them to leave their things behind.)
2. First, create the female histogram.
1. In creating the histogram, each row of the classroom should represent one inch of the possible range of inches, such as 4'10", 4'11", 5', 5'1", and so on.
2. Ask the females "which one of you thinks you are the shortest female in the class?  and which one of you thinks you are the tallest in the class?"  (So far, my students have always gotten a nice chuckle out of this process;  however, I sometimes worry that students may be self-conscious about their height.)
3. Once you've identified the shortest female (she is 4'11", say), ask her to sit in the left-most seat in the first row.
4. Then, move to the second row and the next height, that is, 5'.  Ask the females who are 5' to seat themselves in the first seats of the second row.
5. Proceed until you have placed all of the females in a seat.  When students are seating themselves, make sure that they sit right next to each other in each row.  (You have to keep on reminding the students of this, because they tend to not want to sit right next to eachother.)  Also, make sure that you leave rows, in which no students are of that height, empty.
3. Once the females are all seated, you can use the histogram to illustrate numerous concepts.  By now, the male students are usually ready for some attention (!), so I address the concepts by asking the males, who have a bird's-eye view of the histogram, various questions, such as: "what is the 'average' female height?", "are there any unusual or extreme heights?", "what is the shape of the histogram?", "how do the heights vary?".
4. Then, create a male histogram similarly.  If you have a large classroom (seats 170 or more) and attendance is low (80 or fewer), you should be able to create a histogram alongside the female histogram, by placing the males in the right-most seats of each row.  (I prefer to do this activity in my 3:35 pm class on a Friday of a big home football game, anyway, so the movement of students is more manageable than on a day in which attendance is high.)  If you can create a side-by-side histogram, then it is best to keep the row heights the same for both the male and female histograms.  If there are too few rows in the classroom for the range of student heights, it may be better to ask the female students to vacate the seats, and to create the male histogram in the left-most seats, relabeling the rows as necessary.  (But, in this case, before the females move, ask the students to keep an image of the female histogram in mind, so you can make comparisons to the male histogram.)
5. Once the male histogram is created, you can compare the two histograms.  To feign fairness (!), I generally ask the females the questions now, such as:  "do the 'average' heights appear to differ?", "do the heights of the males vary more, less, or the same as the females?", and so on.
6. Once discussion is completed, give students a chance to return to their original seats if they so wish to move.

Supplementary materials: None.