Mean, median, mode, range, and whisker plot

Date December 2005
Class Algebra
Teacher Lanette VonSeggern

Wrestling with Averages since it is the end of the quarter (I always try to give the students a thinking extra credit assignment), wrestling season, and my algebra students are working on graphing linear equations I thought of this activity.

The students were very diligent in discovering the 10 weights.  They liked discussing the various answers that worked for the situation described.  I related this to graphing linear equations – each person can pick a different three points but since there are infinite ordered pairs as solutions – the line will be graphed the same.  Some students tried to come up with an equation but most students simply used guess and check. 

I liked the way this problem allowed for a variety of methods to solve the problem and reinforced that there are infinite solutions to a given problem – even traveling to a city can have infinite possible routes – it is always better to plan ahead – especially in Nebraska in the winter time!
Date December 2005
Class Calculus
Teacher Ray Weier

How High Can You Jump activity, a classroom set of TI-83 Plus calculators, several CBL units with light probes, the JUMP program from Real World Mathematics Activity by Texas Instruments.  It also came with sample data of 33 jump heights.
I reviewed the terms minimum, maximum, range, mean, median, and mode with them.
My two calculus classes consist of 8 and 6 students so I did the activity in two steps.  First, each student used the JUMP program to record his/her hang time and vertical jump.  We combined all the class jumps, recorded the data on one white-board and looked at finding the minimum, maximum, range, median, and mode by hand.  We then entered the class jumps into each of the student’s calculators, Stat-Plotted the points on a “friendly window”, and then used Stat-Calc to fit a linear regression equation to the data.  At this point, I also demonstrated how to use Stat-Calc to do the one-variable stats for our class data.
For the second part of the activity, we took our class data and combined it with the sample data that came with the JUMP program.   We now had approximately 40 jumps entered into the lists of our calculators.  Using this new data we went through as a group with each student having their own calculator and sorted the data.  We then calculated the one-variable stats again. We looked at the lower and upper quartiles, mean, median, and mode.  We also made a box-and-whiskers plot to get a statistical picture of the data.  We discussed what outliers were and since one of the students in one of the classes was on crutches (from volleyball) and did not actually jump, we decided to enter her in as having a jump of 1 inch just to see the effect that had on the plot as well as the other statistics.
As the final part of the second activity we also made a histogram and then discussed the similarities and differences between the two plots.
Summary:  The JUMP program is really user friendly and worked very well.  I like that it gives you the option of either keeping your current jump or trying another.  Most students wanted to try again to see if they could do better.  Also, sometimes a student would not land in the path of the light beam when jumping so it was nice to be able to throw that jump out and try again.

Date November
Class eighth grade math class
Teacher Becky Bruening

We did the JUMP activity with my the TI-83, CBL and light probe.  I forgot to bring a mag-light flashlight along to school with me, so borrowed a cheap flashlight from the office.  It also worked just fine.

Some students were hesitant to jump, while others couldn’t get enough, so for those who preferred not to jump we just asked for a volunteer to go in their place, and ended up with more than enough data.  We also found that students had to start with their feet together (not one behind) and jump straight up, or they would not land back into the light beam.  This decreased some of their jump heights from what they might attain in a PE class.

Upon collecting our data we computed the mean, median, mode and range as this is what our lesson was covering.  Students were allowed to use a scientific calculator to add and divide, but we didn’t discuss any of the statistical keys.   Later when we discuss quartiles and box-whisker plots I may repeat the activity.

It was a great activity for a group that for the most part has already mastered mean, median, mode and range.  It definitely put some fun into a review lesson.  If it was the first time these topics were being presented however, it may be more of a distraction than an enrichment.
Date Sept. 30, 2005
Class Juniors
Teacher LouAnn Kneifl
Notes I tried the human box and whisker plot with my students.  I had all the juniors together.  We worked with the distance the students lived from school. The first question the students handled was how to work with blocks and miles. We stepped out our number line giving them an opportunity to work with their estimation skills also. They had to consider minimum and maximum and the distance available to work with. When we returned to the room, I had them do a box and whisker plot with another set of data.    Most all the students could do it on paper.   It was interesting to hear some of the students refer to the outside activity while doing the inside one.  The only concern I have is, half of our students live so close to the school and were bunched together, and everyone else very spread out. Our first quartile and the minimum were the same.