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Homework - Measures of Relative Standing

DIRECTIONS: When computation is required, be sure to show all work neatly. Include clear and well labeled diagrams explaining the logic to your answers.

Problems

  1. Considering the expected scores for Exam 1 data set (the first example in the section on grouped frequency distributions), What is the percentile rank of a score of 65? What is the score at the 80th percentile point? (5 points for each question = 10 points)

  2. Consider Juan's scores on his first two tests in college. He received a 75 in Biology and a 85 in Psychology. What follows are some summary statistics from the two tests. Which grade do you think Juan was happier with? (Note that we demonstrated two ways to solve this type of problem in class, one of which was considerably easier than the other.) (10 points)
     
    General
    Biology
    General
    Psychology
    mean
    71
    81
    SD
    20
    10

  3. Consider the following data for the heights of players (in inches) on two basketball teams. (10 points)

     
    Chicago
    Bulls
    Milwaukee
    Bucks
    mean
    76
    78
    SD
    2
    4

    Now assume that the tallest player on the Bull's team is 6'10" and the tallest player on the Buck's team is 7'2". Which player would stand out more from the other players on their respective teams?
  1. A distribution has a mean of 72 and a standard deviation of 16. For each part of the problem, be sure to include the appropriate diagrams with appropriate shading and labeling to clearly show the strategy you used to solve the problem (just like we have been doing in class).

    1. What is the percent of folks scoring between a z of -1.5 and +2? (10 points)
    2. What is the percent of folks scoring between 60 and 70? (15 points)
      How many students would be expected to score within this range in a typical class (N=25)?
    3. What is the percentile rank of a score of 65? (10 points)
    4. What is the score at the 80th percentile point? (10 points)

  2. In a IQ distribution (mean=100, standard deviation=15), how many people would we expect to have an IQ above 130 living in Stevens Point? Note that this problem makes two assumptions. First, Stevens Point has a population of 23,000 people. The second is that folks in Stevens Point are representative of the population as a whole. (15 points)

Multiple Choice (10 points)

  1. A z score is
    a. a deviation that is standardized for all groups.
    b. the number of standard deviations that a given score deviates from the mean.
    c. the mean minus the median divided by the standard deviation.
    d. a standard deviation.

  2. What percent of the distribution falls between the mean and a z score of -1.00?
    a. 13.59
    b. 34.13
    c. 47.72
    d. 50.00

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Comments? mplonsky@uwsp.edu.