Question

Exercise One

The final grades in immunology at State University are recorded in the accompanying table (ranged from a possible 0 to 80; Also See Problem 13):

           29   74 51    42   55   75   74   74   79   74    43   79   55   74   25   04   69   78   74   52

           76 74   04    64   76   79   69   77   79   24    75   78   74 69   65   80   72   79   62   79

           08   66   79    43   76   72   45   73   05   79    74   74   75   38   60   02   74   78   79   73

           63   45   74    64   63   75   62   43   67   72    62   62   54   03   45   79   62   64   75   72

     From the above data (80 cases):

1. (5 pts.) construct a frequency table, include relative frequency and cumulative relative frequency.
2. (8 pts.) Construct a histogram and frequency polygon.
3. (2 pts.) Why did you select the intervals you used for your table and graphs?
4. (2 pts.) Is the above distribution skewed? Explain your answer.

(3 pts.) Define skewed. Demonstrate what that would look like graphically. Why is skewed data problematic?

(3 pts.) What is the relation between kurtosis and variability of the data?

(2 pts.) What do measures of central tendency not tell us? Demonstrate this problem graphically.

(11 pts.) Find the mean, median, and mode for all 80 cases in problem #9. Imagine that you are a graduate teaching assistant for the course. What does you tell us the professor about the students' performance in immunology? Be specific. (Note: The instructor uses a grading scale of A=72-80; B=63-71; C=54-62; D=45-53; F=44 or less.)

Answer 1

construct a frequency table, include relative frequency and cumulative relative frequency.

Frequency Table
Class	Freq	Relative freq	Cumulative relative freq
0-11	6	0.075	0.075
12-23`	0	0	0.075
24-35	3	0.0375	0.1125
36-47	8	0.1	0.2125
48-59	5	0.0625	0.275
60-71	17	0.2125	0.4875
72-83	41	0.5125	1
Total	80

Construct a histogram and frequency polygon.

Your Histogram
Mean	61.425
Standard Deviation (s)	21.16348
Skewness	-1.61184
Kurtosis	1.78951
Lowest Score	2
Highest Score	80
Distribution Range	78
Total Number of Scores	80
Number of Distinct Scores	33
Lowest Class Value	0
Highest Class Value	83
Number of Classes	7
Class Range	12