Statistical Methods for Psychology

Exercises 61

2.38 In one or two sentences, describe what the following graphic has to say about the grade
point averages for the students in our sample.

Histogram for Grade Point Average

2.39 Use SPSS to superimpose a normal distribution on top of the histogram in the previous ex-
ercise. (Hint: This is easily done from the pull-down menus in the graphics procedure.

2.40 Calculate the range, variance, and standard deviation for the data in Exercise 2.1.

2.41 Calculate the range, variance, and standard deviation for the data in Exercise 2.4.

2.42 Compare the answers to Exercises 2.40 and 2.41. Is the standard deviation for children sub-
stantially greater than that for adults?

2.43 In Exercise 2.1, what percentage of the scores fall within plus or minus two standard devia-
tions from the mean?

2.44 In Exercise 2.4, what percentage of the scores fall within plus or minus two standard devia-
tions from the mean?

2.45 Given the following set of data, demonstrate that adding a constant to, or subtracting a con-
stant from, each score does not change the standard deviation. (What happens to the mean
when a constant is added or subtracted?) [5 4 2 3 4 9 5].

2.46 Given the data in Exercise 2.44, show that multiplying or dividing by a constant multiplies
or divides the standard deviation by that constant. How is this related to what happens to the
mean under similar conditions?

2.47 Using the results demonstrated in Exercises 2.45 and 2.46, transform the following set of
data to a new set that has a standard deviation of 1.00: [5 8 3 8 6 9 9 7].

2.48 Use your answers to Exercises 2.45 and 2.46 to modify your answer to Exercise 2.46 such
that the new set of data has a mean of 0 and a standard deviation of 1. (Note: The solution
of Exercises 2.47 and 2.48 will be elaborated further in Chapter 3.)

Grade Point Average

4.00

3.75

3.50

3.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

1.25

1.00

.75

14

12

10

8

6

4

2

0

Std. Dev = .86

Mean = 2.46

N = 88.00