Glendale Community College Measures of Central Tendency Statistics Problems

Part 2 – Generate Your Data (10 Points)

How to do this part of the homework

Step 1: You need 30 small pieces of paper (about 1 inch in length and width, although the exact size is not as relevant). On each piece of paper you write a number, starting with 1 all the way to number 30. So each piece of paper has a unique number. Fold each piece of paper and place them in a bowl, or cup, or a small box, or any container that allows you to mix up the pieces of paper easily:

Step 2:Mix the pieces of paper, and randomly pick two pieces from the pile. Find the average of the two numbers that you drew. For example, if you drew numbers 6 and 23, then you find the average by [(6 + 23)/2]= 14.5; If you drew 20 and 23, then your average is 21.5, etc. Record the average. Then place the two numbers back into the pile. Repeat his process 30 times, each time placing the numbers that you picked back into the pile, mixing the pieces of paper, so that each time you are randomly picking two numbers from 1 to 30. By the end you have generated 30 scores (X1, X2, X3, X4,…….X30), each score being the average of the two numbers you picked randomly each time (Let’s call this Student Generated Data Set, or SGDS). Note that the lowest possible value in SGDS could be 1.5, if you pick numbers 1 and 2; and the highest possible value could be 29.5, if you pick numbers 29 and 30 randomly;

Step 3: What are the measures of central tendency (Mean, Median, and Mode) of SGDS (X1, X2, X3, X4,…….X30)?  (Some of you might end of with a data set that does not have a mode. In that case just write “There is no Mode.”

Step 4: What is the standard deviation of SGDS?