Understanding Mean, Median, and Standard Deviation

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Chapter 2

  1. For the following scores, find the:
    1. Mean: 2
    1. Median: 2
    1. SS: 56
    1. Variance: 2.67
    1. Standard Deviation: 1.67
  2. For the following scores, find the:
    1. Mean: 1312.40
    1. Median: 1361
    1. SS: 76089.20
    1. Variance: 15217.84
    1. Standard Deviation: 123.36
  3. For the following scores, find the:
    1. Mean: 3.17
    1. Median: 3.25
    1. SS: .53
    1. Variance: .09
    1. SD: .30
  4. A psychologist interested in political behavior measured the square footage of the desks in the official office of four U.S. governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, and 36 square feet.
    1. Governors: M=43, SD=5.92 & CEO’s: M=44, SD=10.95
    1. The mean is the average size of the desks in each group of scores (i.e. CEO’s and Governors). Conversely, the standard deviation is how much the scores deviate from the mean for the distribution.
    1. In the examples the mean does not vary much between the two distributions. This would seem to indicate that the average size of the desks of governors and CEO’s is about the same. However, the standard deviation is much higher for the CEO’s indicating that with the distribution the scores vary widely from the mean; whereas, the scores within the distribution of governor’s desks sticks pretty close to the mean.
  5. Explain the results to a person who has never had a course in statistics: The table seems to explain that even though participants were slowest, on average, to identify a tool in the hand of a black person, the participant’s scores varied the greatest when trying to identify the white person with the gun. Likewise, when the participants were asked to answer as quickly as possible they were quickest to identify the white person with the gun, and slowest to identify the black person with the tool, with less deviation on both sides than in experiment 1. Overall, these scores seem to explain that the greatest ambiguity was felt about identifying the white person with the gun and even though it took the longest time in experiment 1 for the participant to identify the tool with the black person the deviation is low, meaning less ambiguity. In conclusion, in both experiments participants quickly identified the gun to both black and white individuals; whereas, it took longer to identify the tool to both black and white individuals. This could be partly explained if the participants were shown different tools and the same gun.
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Chapter 3

  1. On a standard measure of hearing ability, the mean is 300 and the standard deviation is 20. Give the Z scores for persons who score:
    1. 2
    2. .5
    3. -2
    4. 348
    5. 330
    6. 300
    7. 210
  2. A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative ability. For the verbal ability test, the mean for people in general is 50 and the standard deviation is 20. For the quantitative ability test, the mean for people in general is 0 and the standard deviation is 5. Which is this person’s stronger ability: verbal or quantitative? Explain your answer to a person who has never had a course in statistics. Well, in comparison to the other students the z-score for the verbal test was 1.55 and the z-score for the quantitative test was 1.28. This means that the person’s score on the verbal test deviated further from the mean than the score on the quantitative test. Since the deviation for both test scores is positive and the z-score for the verbal test is higher, that would mean that the person scored higher on the verbal test. 
  3. Suppose you want to conduct a survey of the attitude of psychology graduate students studying clinical psychology towards psychoanalytic methods of psychotherapy. One approach would be to contact every psychology graduate student you know and ask them to fill out a questionnaire about it.
    1. Haphazard Selection
    2. The downfall is that the sample can sometimes vary greatly from the population, because the selection of the sample is not truly random.
  4. You are conducting a survey at a college with 800 students, 50 faculty members, and 150 administrative staff members. Each of these 1,000 individuals has a single listing in the campus phone directory. Suppose you were to cut up the directory and pull out one listing at random to contact. What is the probability it would be
    1. P=.8
    2. P=.05
    3. P=.15
    4. P=.2
    5. P=.85
    6. Probability is the chance that a particular category of choices will be made at random. The P-values (probability values) of the aforementioned categories express the chances that a student, faculty member, and an administrative (a, b, and c respectively) will be chosen at random.  

References

Aron, A., Aron, E., & Coups, E. (2006). Statistics for psychology (4th ed.). Upper Saddle River, NJ: Pearson/Allyn Bacon.

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