Statistical Assignment

1. Indicate which scale of measurement each of the following variables reflects:

 

1. Reaction time
2. Urbanicity (where 1 = urban, 2 = suburban, and 3 = rural)
3. The numbers on soccer players’ jerseys
4. Scholastic Assessment Test (SAT) score
5. Type of psychotherapy
6. University ranking (in terms of library holdings)
7. Class size
8. Religious affliation (1 = Protestant, 2 = Catholic, 3 = Jewish, ect)
9. Restaurant rating (* to ****)
10. Astrological sign
11. Miles per gallon

 

2. Imagine the data below are the GPAs for a sample of 60 sophomores at your university. Prepare a relative frequency distribution (use proportions), using an interval width of .30 and .90-1.19 as the score limits for the lowest interval.

3.08    1.81     3.63     2.52     2.97     3.48     1.00     2.70     2.95     3.29

1.40     2.30     4.00     2.69     2.92     3.34     3.00     3.37     3.01     2.11

2.36     3.23     2.99     2.61     3.02     3.27     2.65     3.89     1.60     2.31

3.93     2.98     3.59     3.04     2.88     3.76     2.28     3.25     3.14     2.85

3.45     3.20     1.94     3.80     2.58     3.26     2.06     3.99     3.06     2.40

2.44     2.81     3.68     3.03     3.30     3.54     3.39     3.10     3.18     2.74

 

3. For each of the following sets of scores, find the mode, the median, and the mean:

 

1. 12, 10, 8, 22, 8
2. 14, 12, 25, 17
3. 10, 6, 11, 15, 11, 13

 

4. Consider the four sets of scores:

 

1. 8, 8, 8, 8, 8
2. 6, 6, 8, 10, 10
3. 4, 6, 8, 10, 12
4. 1004, 1006, 1008, 1010, 1012

 

• Upon inspection, which show(s) the least variability? The most variability?
• For each set of scores, compute the mean; compute the variance and standard deviation directly from the deviation scores.
• What do the results of 4-2 suggest about the relationship between central tendency and variability?