Pause problem
Time to Practice 1. Why is the range the most convenient measure of dispersion, yet the most imprecise measure
of variability? When would you use the range? 2. Fill in the exclusive and inclusive ranges for the following items.
High Score Low Score Inclusive Range Exclusive Range
12.1 3
92 51
42 42
7.5 6
27 26 3. Why would you expect more variability on a measure of personality in college freshmen than
you would on a measure of age?
(Continued)
54 Part II ■ Σigma Freud and Descriptive Statistics 4. Why does the standard deviation get smaller as the individuals in a group score more similarly
on a test? And why would you expect the amount of variability on a measure to be relatively
less with a larger number of observations than with a smaller one? 5. For the following set of scores, compute the range, the unbiased and the biased standard
deviations, and the variance. Do the exercise by hand.
94, 86, 72, 69, 93, 79, 55, 88, 70, 93 6. In Question 5, why is the unbiased estimate greater than the biased estimate? 7. Use SPSS to compute all the descriptive statistics for the following set of three test scores
over the course of a semester. Which test had the highest average score? Which test had the
smallest amount of variability?
Test 1 Test 2 Test 3
50 50 49
48 49 47
51 51 51
46 46 55
49 48 55
48 53 45
49 49 47
49 52 45
50 48 46
50 55 53 8. For the following set of scores, compute by hand the unbiased estimates of the standard
deviation and variance.
58
56
48
76
69
76
78
45
66 9. The variance for a set of scores is 36. What is the standard deviation, and what is the range?
(Continued)
Chapter 3 ■ Understanding Variability 55
10. Find the inclusive range, the sample standard deviation, and the sample variance of each of
the following sets of scores:
a. 5, 7, 9, 11
b. 0.3, 0.5, 0.6, 0.9
c. 6.1, 7.3, 4.5, 3.8
d. 435, 456, 423, 546, 465
11. This practice problem uses the data contained in the file named Chapter 3 Data Set 3. There
are two variables in this data set:
Variable Definition
Height Height in inches
Weight Weight in pounds
Using SPSS, compute all of the measures of variability you can for height and weight.
12. How can you tell whether SPSS produces a biased or an unbiased estimate of the standard
deviation?
13. Compute the biased and unbiased values of the standard deviation and variance for the set of
accuracy scores shown in Chapter 3 Data Set 4. Use SPSS if you can; otherwise, do it by hand.
Which one is smaller, and why?
14. On a spelling test, the standard deviation is equal to 0.94. What does this mean?
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