 |  Statistics for the Behavioral Sciences, 4/e Michael Thorne,
Mississippi State University -- Mississippi State
Martin Giesen,
Mississippi State University -- Mississippi State
Measures of Dispersion and Standard Scores
Problems- Markus says that the AD of the following test scores is 2.5, but Karl says it is 1.45. Who is correct?
What are R, sapprox, s2, and s?
| X | f |
| | 25 | 1 | | 24 | 2 | | 22 | 3 | | 21 | 4 | | 20 | 4 | | 19 | 2 | | 18 | 1 |
- In a logic course, 23 students are given 10 word-analogy problems to solve in 5 minutes. The number
of problems correctly solved is recorded for each student. The data are as follows:
| X | f |
| | 10 | 1 | | 9 | 2 | | 8 | 1 | | 7 | 4 | | 6 | 6 | | 5 | 5 | | 4 | 2 | | 3 | 1 | | 2 | 1 |
- Find R, sapprox, s2, and s.
- Plot a frequency polygon of the data and lay off the value of s on it. To simplify your graph, round s and
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- Scores on an experimental psychology test were as follows:
| X | f |
| | 100 | 1 | | 96 | 1 | | 92 | 3 | | 84 | 2 | | 83 | 1 | | 80 | 2 | | 79 | 1 | | 76 | 1 | | 63 | 1 | | 35 | 1 |
Find R, sapprox, s2, and s. What is the z score for a raw score of 96? What score is 2 standard deviation units below the mean? - Using the following frequency distribution, demonstrate that (SfX)2 is not equivalent to SfX2. Compute R, sapprox, s2, and s.
- There are two applicants for the job as test pilot for experimental jet aircraft. Both applicants are given
a reaction-time test and are found to have the same average times. Which applicant should get the job
if consistency of reaction is an important criterion?
| Applicant A | Applicant B | | X | f | X | f |
| | 1.04 | 1 | 1.04 | 1 | | 1.03 | 1 | 0.85 | 1 | | 0.95 | 2 | 0.84 | 2 | | 0.88 | 1 | 0.80 | 2 | | 0.85 | 2 | 0.77 | 3 | | 0.78 | 2 | 0.75 | 3 | | 0.74 | 1 | 0.74 | 2 | | 0.70 | 1 | 0.72 | 1 | | 0.65 | 3 | 0.70 | 2 | | 0.60 | 4 | 0.57 | 1 | | 0.55 | 2 | 0.55 | 2 |
- Participants in an employee training program are tested after 1 week. By company policy, employees who score 1 standard deviation or more below the mean are required to take another week of training. Which employees must receive more training, and which are released from the program?
| X | f |
| | 92 | 1 | | 91 | 1 | | 88 | 3 | | 87 | 3 | | 81 | 4 | | 79 | 5 | | 77 | 5 | | 76 | 3 | | 71 | 3 | | 69 | 2 | | 53 | 1 | | 51 | 2 | | 47 | 1 | | 44 | 1 | | 39 | 1 |
- Using the following data, find s2. Determine s and plot it on the baseline of a frequency polygon. For
ease in plotting, round the mean and standard deviation to the nearest whole numbers.
| X | f |
| | 28 | 1 | | 27 | 1 | | 26 | 3 | | 25 | 5 | | 24 | 5 | | 23 | 2 | | 22 | 1 | | 21 | 1 | | 20 | 1 |
Assuming a mean of 2.57 with a standard deviation of 0.83, answer the following questions: - What is the z score for a raw score of 3.75?
- What is the z score for a raw score of 2.10?
- How far from the mean in standard deviation units is a score of 1.3?
- What score lies 1.75 standard deviation units above the mean?
- What score lies 2.17 standard deviation units below the mean?
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