Teacher: Alicia Klaassen

Class: Pre-Algebra 8th Grade

What I Did: The activity was created to help the inexperienced students become a little more familiar with the graphing calculator and also to show them that a calculator can be used as an aide when doing long and involved calculations (specifically like those in statistics problems). We began the activity together (after they already knew how to find mean and median on their own without the use of a calculator). We discussed the steps and the important buttons and function on the calculator. We went through the example together. Then they were to complete the practice problems on their own.

What the Students Did: I really liked the way that these students—most of them—felt comfortable with the graphing calculator almost immediately. They seemed to catch on pretty quickly and liked letting the calculator do the work for them. I didn’t have too many problems until they began question 6. Most didn’t catch on to the fact that the mean was affected by a large outlier and the median wasn’t affected as much. I did not suggest this idea when we worked the problems and had hoped that they would catch it on their own.

What I would Change: I would let the students work the same way that they did. I may not give them as much guidance next time. Maybe when we move on the questions 5 & 6 I will have them look up the answer in another math book or on the internet—maybe even have them make up their own examples to see what happens.

Activity Extension: I would add a section where the students have to come up with their own task to find real life data available to them here at school. Maybe have them keep track of the outside temp for a few weeks, or actually poll students at school to find out about allowances. Then they can see how the mean and median is put to work in real life. I may even try to make a Human box plot of the information like we did in our workshop.

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Graphing Calculator Investigation: Mean and Median on a TI-83 Plus Calculator

Name:_________________________________________ Date:______________

A graphing calculator is able to perform operations on large data sets efficiently.

Steps to Find the Mean and Median using a TI-83 Plus calculator

  1. Enter the data into a list.

Š      Get to the list by pushing STAT and then choosing option 1: Edit

Š      Clear any existing lists by moving the cursor to the top of the column (over the list name like L1, L2, etc.) and then push CLEAR and then ENTER.

Š      To get the numbers into the list, type in the first number from the list and push ENTER to move to the next row. Next, type in the second number from the list and push ENTER. Follow this procedure until all numbers in your data list are entered in the list column in your calculator. (Remember to use all the numbers in the list. If a number is repeated in the original data, be sure to type it in the list twice. If the number has a negative sign, be sure to type in a negative sign before the number.)

  1. Push 2nd MODE (to quit and get back into the regular screen).
  2. Display the one variable statistics on your calculator screen by pushing STAT, then move the cursor over one position to the CALC column, and choose option 1: 1-Var Stats.
    • The mean is represented by
    • The median is represented by Med
    • You may use the down/up arrow keys to move between them.

Example 1: Seventh Graders were surveyed and asked what their weekly allowance (in dollars) was. The results are shown in the table below.

20

10

5

5

10

15

5

10

5

10

5

5

5

5

5

0

10

12

3

15

Find the mean and median allowance.

Practice Problems

In problems 1 – 4 find the mean and median of each set of data by using your TI-83 Plus Calculator as an aid. Round decimal answers to the nearest hundredth.

1. 6.4, 5.6, 7.3, 1.2, 5.7, 8.9

            mean =

            median =

2. -23, -13, -16, -21, -15, -34, -22

            mean =

            median =

3. 123, 423, 190, 289, 99, 178, 156, 217, 217

            mean =

            median =

4. 8.4, 2.2, -7.3, -5.3, 6.7, -4.3, 5.1, 1.3, -1.1, -3.2, 2.2, 2.9, 1.4, 68

            mean =

            median =

5. Look back at the medians found in problems 1 – 4. When is the median value a member of the data set?

6. Refer to problem 4.

            a.) Which statistic better represents the data, the mean or median? Explain.

            b.) Suppose the number 68 should have been 6.8. Recalculate the mean and

            median. Is there a significant difference between the first pair of values and

            the second pair? Explain.

            c.) When there is an error in one of the data values, which statistic is less likely to

            be affected? Why?