PROBLEMS 3.1. Find the median for the following sets of scores. a. 2, 5, 15, 3,9 b. 9, 13, 16, 20, 12, 11 c. 8, 11, 11, 8, 11, 8 3.2. Which of the following distributions is bimodal? a. 10, 12, 9, 11, 14, 9, 16, 9, 13, 20 b. 21, 17, 6, 19, 23, 19, 12, 19, 16, 7 c. 14, 18, 16, 28, 14, 14, 17, 18, 18, 6 *3.3. Refer to problem 2.2, the political scientist's yard-sign data. a. Decide which measure of central tendency is appropriate and find it. b. Is this central tendency measure a statistic or a parameter? c. Write a sentence of interpretation. *3.4. Refer to problem 2.1. Find the mean, median, and mode of the heights of both groups of Americans in their 20s. Work from the Appendix G answers to problem 2.1. 3.5. For distribution a, find the median starting from the bottom. For distribution b, find the median starting from the top. The median of distribution c can probably be solved by inspection. a. X f b. 4, 0, -1, 2, 1, 0, 3, 1, -2, -2, - 1, 2, 1, 3, 0, -2, 1, 2, 0, 1 15 4 C. 28, 27, 26, 21, 18, 10 3 13 5 12 4 11 2 10 3.6. What two mathematical characteristics of the mean were covered in this section? 3.7. For each of the following situations, tell which measure of central tendency is appropriate and why. a. As part of a study on prestige, an investigator sat on a corner in a high-income residential area and classified passing automobiles according to color: black, gray, white, silver, green, and other. b. In a study of helping behavior, an investigator pretended to have locked himself out of his car. Passersby who stopped were classified on a scale of 1 to 5 as (1) very helpful, (2) helpful, (3) slightly helpful, (4) neutral, and (5) discourteous. c. In a study of household income in a city, the following income categories were established: $0-$20,000, $20,001-$40,000, $40,001-$60,000, $60,001-$80,000, $80,001-$100,000, and $100,001 and more. d. In a study of per capita income in a city, the following income categories were established: $0-$20,000, $20,001-$40,000, $40,001- $60,000, $60,001-$80,000, $80,001-$100,000, $100,001-$120,000, $120,001-$140,000, $140,001-$160,000, $160,001-$180,000, and $180,001-$200,000. e. First admissions to a state mental hospital for 5 years were classified by disorder: schizophrenic, delusional, anxiety, dissociative, and other. f. A teacher gave her class an arithmetic test; most of the children scored in the range 70-79. A few scores were above this, and a few were below. 3.8. A senior psychology major performed the same experiment on three groups and obtained means of 74, 69, and 75 percent correct. The groups consisted of 12, 31, and 17 participants, respectively. What is the overall mean for all participants? ermine the direction of skew of the expenditure data
