Homework 2

HOMEWORK 2 Homework 2 Brandi Kuhn CBU

Week 2 HOMEWORK Week 2 Homework Chapter 3 1. Why is the range the most convenient measure of dispersion, yet the most imprecise measure of variability? When would you use the range? ANSWER: Due to its single computation of the difference between the highest and lowest numbers in a distribution, the range is the most efficient method to measure dispersion. The imprecision stems from its inability to consider values that lie in the middle of a distribution's range. Range would be used when roughly estimating the variability of a distribution.  2. Fill in the exclusive and inclusive ranges for the following items. Be sure to show your work below. High Score Low Score Inclusive Range Exclusive Range (r = h – l +1) (r = h – l) 7 6 7 − 6 + 1 = 2 7 − 6 = 1 89 45 89 − 45 + 1 = 44 89 − 45 = 44 34 17 34 − 17 + 1 = 18 34 − 17 = 17 15 2 15 − 2 + 1 = 14 15 − 2 = 13 1 1 1 − 1 + 1 = 1 1 − 1 = 0 3. Why would you expect more variability on a measure of personality in college freshman than you would on a measure of height? ANSWER: The height of most adults, or people in college, falls between a much smaller range than that of varying personalities. There are many more variables when measuring personality types. 4. Why does the standard deviation get smaller as the individuals in a group score more similarly on a test? ANSWER: As the group's test scores increase in similarity, they become more consistent and less deviated, bringing the scores themselves closer to the mean, or average, score. This would

Week 2 HOMEWORK result in a smaller standard deviation by decreasing the difference between the scores and the subtracted mean. 5. For the following set of scores, compute the range, the unbiased and the biased standard deviations, and the variance. Use SPSS for this question but there may be some part of it you will have to do by hand. 31, 42, 35, 55, 54, 34, 25, 44, 35 Statistics VAR00001 N Valid 9 Missing 0 Std. Deviation 10.18714 Variance 103.778 Range 30.00 Biased Standard Deviation = 9.60 Unbiased Standard Deviation = 10.19 (rounded to the second decimal place) 6. The variance for a set of scores is 25. What is the standard deviation, and what is the range? ANSWER: Since the variance is the standard deviation squared, then the standard deviation would be 5. Range is unknown without available data set or mean.