Data Collection and Descriptive Statistics

This homework has two parts. In the first part, you will be asked to compute a number of statistics given a set of raw data. In the second part, you will be asked to answer a set of questions related to the calculation of and interpretation of a Z score. Please show your work. You may use a spreadsheet and turn this in with your answers.

PART I

Researchers were interested in examining the number of stressful events experienced by college students. They collected data from two groups of students: freshman and juniors. The instrument they used to collect the data was a simple checklist that asked the student to "Check every item that has occurred to you in the last 3 months." There were 100 items; sample items are "I moved," "I got married," "Someone close to me died," "I started a new job".

Use the data below to answer the questions that follow:

Freshman Data Set

1. Compute the Mean.
2. Compute the Median.
3. What is the Mode?
4. Compute the range.
5. Compute the standard deviation (see page 156 of the text; you may use a spreadsheet program such as excel for this problem, just be sure you include this in your assignment).
6. What is the variance?
7. Using what you learned in Chapter 7, how would you describe this set of data? In other words, how would you describe the "average" score (mean, median or mode and why)? How would you describe the variability (range, standard deviation, or both, and why)?
   Junior Data Set

   3
   3
   3
   4
   3
   2
   4
   2
   3
   4

8. Compute the Mean.
9. Compute the Median.
10. What is the Mode?
11. Compute the range.
12. Compute the standard deviation (see page 156 of the text; you may use a spreadsheet program such as excel for this problem, just be sure you include this in your assignment).
13. What is the variance?
14. Using what you learned in Chapter 7, how would you describe this set of data? In other words, how would you describe the "average" score (mean, median or mode and why)? How would you describe the variability (range, standard deviation, or both, and why)?
15. Putting it all together: Do Freshman and Juniors report similar numbers of stressful events? How would you say the two groups compare?
    (15) Based on the sample data, it appears that Freshman report more stressful events than Juniors
    PART II
    Answer the following questions. Please refer to the Figure 7.6 on page 159 and the formula on page 160.
    Students were given an exam with 300 multiple-choice questions. The distribution of the scores was normal and mean was 195 with a standard deviation of 30. You may find it helpful to draw out this distribution before answering the questions below (use the example of Figure 7.6 on page 159).
16. What were the scores of the students who were within one standard deviation of the mean?

1. What percent of students did that include?
2. What was the score of students who scored in the middle of the class? (50% did better, 50% did worse).
3. If A’s are given to students who score 90% or above, what is the minimum Z-score of someone getting an A?
4. Let’s say you got 235 on this test. Your colleague is in a different section of this course. Her score was 82 out of 100 on her test. In her section the mean was 72 and the standard deviation was 7. Which one of you did better? (Hint: compare Z-scores.)

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