1. Indicate which scale of measurement each of the following variables reflects: (25 pts.

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

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. (25 pts)

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

Solution

3. For each of the following sets of scores, find the mode, the median, and the mean: (25 pts)

1. 12, 10, 8, 22, 8

Mode = 8

Median = 10

Mean = 12

1. 14, 12, 25, 17

Mode = N/A

Median = 15.5

Mean = 17

1. 10, 6, 11, 15, 11, 13

Mode = 11

Median = 11

Mean = 11

4. Consider the four sets of scores: (25 pts.)

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

1. Upon inspection, which show(s) the least variability? The most variability?

The least variability = a)  8, 8, 8, 8, 8

The most variability = c)  4, 6, 8, 10, 12 and d)   1004, 1006, 1008, 1010, 1012

1. For each set of scores, compute the mean; compute the variance and standard deviation directly from the deviation scores.
2. a) 8, 8, 8, 8, 8

The mean= 8

The variance = 0

Standard deviation = 0

1. b) 6, 6, 8, 10, 10

The mean = 8

The variance = 4

Standard deviation = 2

1. c) 4, 6, 8, 10, 12

The mean = 8

The variance = 10

Standard deviation = 3.16

1. d) 1004, 1006, 1008, 1010, 1012

The mean = 1008

The variance = 10

Standard deviation = 3.16

1. What do the results of 4-2 suggest about the relationship between central tendency and variability?

The results of 4-2 suggest about the relationship between central tendency and variability that central tendency summarizes the whole dataset using a single value that represents a certain aspect of the dataset, for instance, the mean is the average of the sum of the values, the median is the midpoint when the data is arranged in an ascending or descending order while mode shows that value occurring most often in a dataset. On the other hand, variability summarizes how far apart the values in the dataset are distributed from each other. Thus, when the variability is low the values of central tendency have minimal differences, for example when the variability is 0 the mean, median, and mode are all equivalent.