Download Review Session 1

Review Session 1
Central Tendency and Variability
1. The following are the scores of 25 students who participated in a psychology experiment. The scores
represent the number of trials required to complete a memorization test. (Consider the students to be a
sample.)
11 10 12 11 6 15 14 17
9 12
13 14 15 10 11
a. Determine the mean, median, and mode.
b. Determine the range, variance, and standard deviation.
2. Consider the following scores from a sample: 11, 13, 7, 10, 15, 3, 12, 11, 4, 14
a. Determine the mean.
b. Using these data, show that (X – M) = 0.
3. Suppose we add 4 to each of the scores in Problem 2. What effect will this have on the mean and standard
deviation of these scores?
4. Provide graphical illustrations for the frequency distributions from which the following measures of
central tendency were derived. Describe the distributions in terms of symmetry, indicating the direction of
skewness of asymmetric distributions.
a. Mean = 46
b. Mean = 43
c. Mean = 40
Median = 43
Median = 43
Median = 43
Mode = 40
Mode = 43
Mode = 46
5. A marital satisfaction inventory was given to a sample of married persons with and without children.
The following data were obtained.
Male
Female
Male
Female
no children
no children
with children
with children
n
48
63
56
67
Mean
84.3
76.8
58.8
62.6
a. Find the mean of the total group.
b. Find the mean for the females.
c. Find the mean for married persons with
children.
6. The mean of a set of eight scores is 37. The first seven scores are 40, 29, 33, 43, 39, 35 and 40. What is
the eighth score?
Review Session 2
Distributions and Transformations
1. The following list gives test scores from a sample of 30 students.
77
98
83
79
88
73
75
72
76
74
75
88
79
78
79
81
66
67
77
85
75
68
68
75
77
72
76
71
85
85
a. Develop a stem-and-leaf display.
b. Determine the five-member summary.
c. Construct the box plot from the five-number
summary.
2. Determine the transformed scores for the following z scores for a distribution with mean equal to 50 and standard
deviation equal to 10:
2.32, 1.84, 0.00, and – 0.37.
3. Consider the following set of scores.
24 18 20 28 15 25 24 12 26 18 14 20 24 17 16
a. Determine the mean and the standard deviation.
b. Convert each raw score to a standard score.
c. Show that this set of standard scores has a mean equal to 0 and a standard deviation equal to 1.
d. Multiply each of the standard scores by 10 and add 50. Show that the mean of this transformed
distribution has a mean of 50 and a standard deviation of 10.
e. Add 5 to each o f the raw scores. Compute the mean and standard deviation for this new
distribution. Compute z scores for each of these new scores. How do these results differ from
those in Part D.
4. Suppose a distribution has a mean of 18 and a standard deviation of 4 and you want to transform this
distribution to one that has a mean of 100 and a standard deviation of 10. Describe the process. What raw
score in the original distribution corresponds to a transformed score of 115?
5. John took two proficiency tests: one in mathematics, and the other in humanities. His score on the
mathematics test was 40; his score on the humanities test was 115. John’s reference group for the two
tests had the following results:
Mathematics
Mean = 35.2
SD = 4.5
Humanities
Mean = 107.8
SD = 9.6
Relative to the reference group, on which test did John have the highest performance?
6. John took three standardized tests with the following results:
Test
Chemistry
Mathematics
English
Score
Mean
SD
85
82
10
80
75
8
80
90
12
a. Compute a z score for each of John’s test scores.
b. b. What appears to be John’s strongest subject area?