STA 144 Week 2 Homework(1)

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Jan 9, 2024

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STA 144 Week 2 Homework Work on the following problem set from chapters 3-4 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? a. This is because range can determine the difference between the highest and lowest points on the data but cannot give us the differences between each score, so trying to find out how the data is separated is harder but finding out the difference between the highest and lowest is very good. We would use Range when trying to find the difference in heights, or ages. We wouldn’t use range when trying to determine the difference in categories of data sets. 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 7 6 2 1 89 45 45 44 34 17 18 17 15 2 14 13 1 1 1 0 2. Why would you expect more variability on a measure of personality in college freshman than you would on a measure of height? a. Because height is objective and can accurately be measured and verified and has a lower chance of having wild outliers where-as personality is extremely subjective and many people might describe personality in very different ways leading to a far more varied set of responses when compared to hard numbers. 3. Why does the standard deviation get smaller as the individuals in a group score more similarly on a test?

a. Because the variety of scores are lower so the difference between each score becomes smaller as each student is getting closer to the average score. There is less variety among the students to need to account for. 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 VAR00008 N Valid 9 Missing 0 Mean 39.4444 Std. Deviation 10.18714 Variance 103.778 Range 30.00 The Biased Standard Deviation is 9.6045 6. The variance for a set of scores is 25. What is the standard deviation, and what is the range? The Standard Deviation is 5 and the range is about 20

7. Use SPSS to find the range, the standard deviation, and the variance of each of the following sets of scores: a. 3, 5, 7, 9 b. 0.2, 0.4, 0.6, 0.8 c. 3.5, 6.2, 9.3, 4.1, 5.5, 7.9 Statistics VAR000 14 VAR000 13 VAR000 12 N Valid 4 4 6 Missin g 14 14 12 Mean 6.0000 .5000 6.0833 Std. Deviation 2.58199 .25820 2.21848 Variance 6.667 .067 4.922 Range 6.00 .60 5.80 Chapter 4 1. A data set of 50 comprehension scores (named Comprehension Score) called Chapter 4 Data Set 1 is available in Appendix C of your textbook and on the website. Use SPSS to answer the following questions and/or complete the following tasks:

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