The descriptive statistics and histograms displayed on the attached sheet are based on fictitious data on the salaries of teachers in the 50 states and the District of Columbia. The states are grouped into the three regions as listed below.
Region 1 – North
Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New York, New Jersey, Pennsylvania, Ohio, Indiana, Illinois, Michigan, Wisconsin, Minnesota, Iowa, Missouri, North Dakota, South Dakota, Nebraska, Kansas.
Region 2 – South
Delaware, Maryland, District of Columbia, Virginia, West Virginia, North Carolina, South Carolina, Georgia, Florida, Kentucky, Texas, Alabama, Mississippi, Arkansas, Louisiana, Oklahoma, Texas.
Region 3 – West
Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada, Washington, Oregon, California, Alaska, Hawaii.
Data retrieved from http://www.cvgs.k12.va.us/DIGSTATS/Dmain.htmlAnswer questions 1-5 based on the attached information (see final page of this document) on teacher salaries. Please type your answers below each question.
2. In which region is the difference between the mean and the median the smallest? Relate your answer to the shape of the distribution. (Hint: In what type of distribution do we expect the mean to be equal or approximately equal to the median?)3. What is the most common salary interval in each of the three regions? Does the mean salary fall into the most common interval in any of the regions? Does your response to this question surprise you? Why or why not?4. What does the standard deviation reveal about the teachers’ salary data? In which region do the teacher salaries vary the most from the mean? Which region has the most consistent, i.e., least variable, salaries? 5. The range of salaries in Region 3 is considerably wider than the range in the other two regions. Would it be advisable to report the range as the only measure of variability for this region? Why or why not?6. An undergraduate student received a score of 42 on the midterm and a score of 84 on the final in an Introduction to Psychology course. Descriptive statistics on the two exams are listed below.
MEAN STANDARD
DEVIATION NUMBER OF
POINTS
MIDTERM 40.0 3.0 50
FINAL 78.0 5.0 100 a. Compute the students z score on the midterm and on the final b. On which exam did he have a higher standing in relation to other students in the course?7. Use the chart on p. 311 of the textbook to complete this part of the exercise. Listed below are the achievement scores of pairs of students on the same standardized test expressed as two different measures of relative position. Indicate which student in each pair performed better in relation to the norm group.
a. Alan scored in stanine 9; Bobs percentile rank was 82. b. Carols z score was -.5, Darlenes percentile rank was 54. c. Eds percentile rank was 26; Frank scored in stanine 2. d. Gails z score was +1.5; Helens percentile rank was 95.
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