Each section is worth a different number of points, for a total of 100 points.

Part I. Summarizing Data and Measures of Central Tendency

(All work must be shown on a separate sheet.  You may use a calculator, but I need to be able to follow the steps you used.)

 

1.  For the following frequency distribution:  (5 points)

Distribution 1

X

f

9

1

8

2

7

3

6

4

5

5

4

4

3

3

2

2

1

1

 

 

a. Determine the mean, median and mode.

 

b. Construct a frequency polygon and superimpose a smooth curve on the frequency polygon.

 

c. Insert the mean, median and mode of the frequency distribution at the appropriate points.

 

 

 

 

 

2.  For the following frequency distribution:  (5 points)

Distribution 1

X

f

9

0

8

1

7

1

6

2

5

2

4

3

3

4

2

5

1

7

 

a.  Determine the mean, median and mode.

 

b. Construct a frequency polygon and superimpose a smooth curve on the frequency polygon.

 

c. Insert the mean, median and mode of the frequency distribution at the appropriate points.

 

 

 

 

 

 

3.  For the following frequency distribution:  (5 points)

Distribution 1

X

f

9

7

8

5

7

4

6

3

5

2

4

2

3

1

2

1

1

0

 

a.  Determine the mean, median and mode.

 

b. Construct a frequency polygon and superimpose a smooth curve on the frequency polygon.

 

c. Insert the mean, median and mode of the frequency distribution at the appropriate points.

 

 

 

 

 


4.       Which of the distributions above is normally distributed, positively skewed, negatively skewed? (6 points)

 

5.       If these scores represent scores on a 10-item spelling test designed for 8th graders, which distribution would likely result from: a. 5th graders; b .11th graders; c. 8th graders.  (6 points)

Part II. Variability, The Normal Distribution and Converted Scores.

6.       Calculate the mean, median, mode, standard deviation and range of the following sets of measurements:  (20 points)

         a.       9, 7, 6, 6, 2

         b.       12,10,9, 8, 6

         c.       82,82,82,82,82

         d.       12, 10, 9, 8, 6, 45

 

 

7.       Use question number 6 to help answer the following questions: (8 points)

a.       Why is the standard deviation in (d) so large compared to the standard     deviation for question (b)?

b.       Why is the mean so much higher in (d) than in (b)?

c.       Why is the median relatively unaffected?

d.       Which measure of central tendency best represents the set of scores in (d)?

 

8.       Given, a mean of 50, and a standard deviation of 5 calculate the raw score, z-scores, T- scores, and percentile ranks where appropriate.  (20 points)

         a.  Given a raw score of 35, find the z, T and %tile

         b.  Given the z score of 1.2, find the raw score, T, and %tile

         c.  Given the T score of 35, find the raw score, the z score and the %tile

         d.  Given the %tile of 16, find the raw score, z, and T.

 

9.       The Graduate Record Examination (GRE) has a combined verbal and quantitative mean of 1000 and a standard deviation of 200.  Scores range from 200 to 1600 and are approximately normally distributed.  (25 points)

For each of the following problems:

1. Draw a rough sketch, darkening the portion of the cure that relates to the answer,

         2. Indicate the percentage or score called for by the problem.

 

         a. What percentage of persons who take the test score above 1300?

         b. What percentage score above 800?

         c. What percentage score below 1200?

         d. Above what score do about 20 percent of the test-takers score?

         e. Above what score do about 30 percent of the test-takers score?

 

Since the assignment is worth 20 points overall, take the score you earn and divide it by 5 to get the number of points earn toward your final grade. 

 

Return to Syllabus