• When reporting numerical figures,please use one decimal place of accuracy.

Scenario:

Professor Lowiq asked 20 random students from their class of 100 students a question: "On a scale from 0 to 10, with 0 representing 0% and 10 representing 100%, how much does my statistics class entertain you?" The following reflects the data that was recorded:

{x} = [0,1,1,4,4,5,8,8,8,8,9,9,9,9,9,9,9,10,10,10]

Based upon this data, Professor Lowiq made the following conclusion: "On average, only 70% of my class thinks that statistics are useful."

Questions:

1. What is being measured in Professor Lowiq's research?

2. Calculate themean of the data set.

3. a) Calculate themode of the data set. b) In own words, tell me what themode says about the data.

4. a) Calculate themedianof the data set. b) In own words, tell me what themedian says about the data.

5. Is this data set best described using themean,median,or themode? Explain your choice.

6. a) In this scenario, should the standard deviation be calculated as a population (using "N" as the denominator) or as a sample (using "n-1" as the denominator)? Explain your choice. b) Calculate thestandard deviation.

7. Professor Lowiq's conclusion is erroneous. Find and explain three (3) mistakes that Professor Lowiq has made.

8. Re-write Professor Lowiq's conclusion, in own words, in a way that you feel best reflects the data.

Optional Question:

Is the data in this scenario reflective of anormal distribution? Are there anyoutliers in the data set? Explain your responses (showing all calculations you used to reach your conclusions).