Homework 2

  • Due Feb 26, 2023 by 11:59pm
  • Points 20
  • Submitting a text entry box or a file upload
  • File Types pdf
  • Available Feb 20, 2023 at 7am - Feb 26, 2023 at 11:59pm
This assignment was locked Feb 26, 2023 at 11:59pm.

This week's homework has two parts

Please read carefully:

Part 1 (10 Points)

For Part 1 you have 5 problems to do, but each of the problems require time to complete. Please use separate sheet of paper to show your work for each of the problems. It means you must upload 5 sheets to Canvas, each sheet containing the steps you used to find the answers.

For each problem you are required to find:

  • a) the mean,
  • b) the median,
  • c) sum of the squared deviation,
  • d) the variance,
  • e) the unbiased standard deviation (square root of sum of squared deviation divided by n - 1),
  • f) the biased standard deviation  (square root of sum of squared deviation divided by n),
  • g) the inclusive,
  • h) the exclusive range.

For full credit, you MUST show all the steps you have taken to find the answer to the problems. 

I know it is tedious work, but that is the only way I know (and you know) that you can find these statistics on your own without using any statistics software.

Of course you can use your calculator!

 

Problem 1:

4, 2, 0, 5, 1, 4, 2, 3, 0, 0, 1, 4, 4, 0, 1, 4, 3, 3, 2, 1, 0

Problem 2:

1212, 1246, 1361, 1372, 1479

Problem 3:

3.0, 3.6, 2.6, 3.1, 3.9, 3.2

Problem 4:

8, -5, 7, -10, -5

Problem 5:

94, 86, 72, 69, 93, 79, 55, 88, 70, 93

 

 

Part 2 - Generate Your Data (10 Points)

Part 2 requires that you conduct a practical experiment and generate your own data. Each student will end up with a different data set for this assignment. It wastes some paper, but I think it is worth it to learn more about statistics. Please keep pieces of paper as we will do more homework assignments using those pieces. 

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? 

For Part 2, you must include your answers to Step 2, Step 3, and Step 4

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