psychology statistic

Measures of Central Tendency, Measures of Dispersion, Location of Scores

Measures of Central Tendency

1. Find the mean, median, and mode for each of the following sets of scores (3 points per set).

a. 3, 4, 4, 6, 6, 6, 6, 7, 7, 9, 9

b. 6, 8, 5, 5, 8, 9, 6, 28

c. 20, 22, 22, 24, 24, 27, 28, 28, 31

d. -3, -2, 0, 1, -3, -5, 3, 6, 3, 5, -1

2. In which of the sets of scores in question #1 is the mean a poor measure of central tendency? Why? (2 points)

3. In which of the sets of scores in question #1 is the mode a poor measure of central tendency? Why? (2 points)

4. What can we say about the relationship between the mean and median is a positively skewed distribution? In a negatively skewed distribution? (2 points)

5. Calculate the mean of the following set of scores: 3, 1, 3, 4, 5, 5, 7, 9 (3 points each)

a. Add a constant (c=3) to each score and recalculate the mean. In general, what is the effect on the mean when any constant is added to all the scores?

b. Subtract a constant (c=3) from each score and recalculate the mean. In general, what is the effect on the mean when any constant is subtracted from all the scores?

c. Multiply each score by a constant (c=3). Recalculate the mean. In general, what is the effect on the mean when each score is multiplied by any constant?

d. Divide each score by a constant (c=3). Recalculate the mean. In general, what is the effect on the mean when each score is divided by any constant?

6. You have calculated the maximum speed of various race cars. You later discover that all the speedometers were set 5 miles an hour too slow. How will adjusting the speedometers affect the mean, median, and mode of the speeds? (2 points)

Measures of Dispersion

7. For the following sets of scores, calculate the sum of squares, the variance, and the standard deviation (4 points each).

a. 2, 4, 7, 3, 9, 10, 27

b. 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

c. 3, 5, 6, 7, 8, 9, 10, 11

8. Why is the standard deviation in part a of question #7 so large? Describe the effects of extreme deviations on the standard deviation (2 points).

9. Determine the range for each of the set of measurements in question #7. For which of these is the range a misleading index of variability and why (2 points)?

10. Calculate s2 and s for the following set of scores: 3, 5, 9, 3, 8, 2, 6 (4points per set)

a. Add a constant (c=2) to each score and recalculate s2 and s. In general, what is the effect on these statistics when any constant is added to all scores?

b. Subtract a constant (c=2) to each score and recalculate s2 and s. In general, what is the effect on these statistics when any constant is subtracted from all scores?

c. Multiply each score by a constant (c=2) and recalculate s2 and s. In general, what is the effect on these statistics when all scores are multiplied by a constant?

d. Divide each score by a constant (c=2) and recalculate s2 and s. In general, what is the effect on these statistics when all scores are divided by a constant?

11. One sample has a mean of M = 12 and a second sample has a mean of M = 10. The two samples are combined into a single set of scores. (2 points each)

a. What is the mean for the combined set if both of the original samples have n = 7 scores?

b. What is the mean for the combined set if the first sample has n = 3 and the second sample has n = 7?

c. What is the mean for the combined set if the first sample has n = 7 and the second sample has n = 3?

12. For a population with ? = 70 and s = 16

a. the z-score for each of the following X values (1 point each)

i. X = 75
ii. X = 62
iii. X = 54.5
iv. X = 92.3

b. the score (X value) that corresponds to each of the following z-scores (1 point each)

i. z = -.35
ii. z = 1.00
iii. z = -2.00
iv. z = .67

c. the proportion of the normal distribution that is located below the following
z-scores (1 point each)

i. z = -.35
ii. z = 1.00
iii. z = -2.00
iv. z = .67

d. the proportion of the normal distribution that is located above the following z-scores (1 point each)

i. z = -.55
ii. z = 1.00
iii. z = -2.00
iv. z = 1.50

e. the proportion of the normal distribution that is located between the two z-score values (2 points each)

i. z = .75 and z = 1.50
ii. z = -0.50 and z = 0.75
iii. z = -2.00 and z = -0.50

13. A fifth grader takes a standardized achievement test (?= 125, s = 15) and scores a 144. What percentage of children score below this fifth grader? (2 points)

14. Pat and Chris both took a spatial abilities test (? = 80, s = 8). Pat scored a 76 and Chris scored a 94. What percent of individuals would score between Pat and Chris? (2 points)

2. Scores on the SAT form a normal distribution with ? = 500 and s = 100.

a. What is the minimum score necessary to be in the top 10% of the SAT distribution? (2 points)

b. Find the range of values that defines the middle 90% of the distribution of SAT scores. (2 points)