Chapter 3

3.1. Find the mean and median of the following sets of scores. (LOs: 1)

a. 2, 5, 15, 3, 9

Click or tap here to enter text 3.1 a.

b. 9, 13, 16, 20, 12, 11

Click or tap here to enter text 3.1 b.

c. 8, 11, 11, 8, 11, 8

Click or tap here to enter text 3.1 c.

3.2. Find the mode of each set of scores. (LOs:1)

a. 0, 4, 4, 5, 6

Click or tap here to enter text 3.2 a.

b. 12, 7, 10, 12, 11, 9

Click or tap here to enter text 3.2 b.

3.3. What three mathematical characteristics of the mean were described in this section? (LOs: 1)

Click or tap here to enter text 3.3.

3.4. Which of the following distributions is bimodal? (LOs: 1)

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

Click or tap here to enter text for question 3.4.

*3.5. Refer to Problem 2.2 of Chapter 2, the political-scientist student's yard-sign data. (LOs: 2)

a. Decide which measure of central tendency is appropriate and find it.

Click or tap here to enter text for question 3.5 a.

b. Is this central tendency measure a statistic or a parameter?

Click or tap here to enter text for question 3.5 b.

c. Write a sentence of interpretation.

Click or tap here to enter text for question 3.5 c.

*3.6. Refer to Problem 2.1 of Chapter 2. 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. (LOs: 1)

Click or tap here to enter text for question 3.6.

3.7. Find the median of a, starting from the bottom. Find the median of b, starting at the top. The median of distribution c can probably be solved by inspection. (LOs: 1)

a.

X

f

15

4

14

3

13

5

12

4

11

2

10

1

Click or tap here to enter text for question 3.7 a.

b. 4, 0, -1, 2, 1, 0, 3, 1, -2, -2, -1, 2, 1, 3, 0, -2, 1, 2, 0, 1

Click or tap here to enter text for question 3.7 b.

c. 28, 27, 26, 21, 18, 10

Click or tap here to enter text for question 3.7 c.

3.8. For each of the following situations, tell which measure of central tendency is appropriate and why. (LOs: 1)

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.

Click or tap here to enter text for question 3.8 a.

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.

Click or tap here to enter text for question 3.8 b.

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.

Click or tap here to enter text for question 3.8 c.

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.

Click or tap here to enter text for question 3.8 d.

e. First admissions to a state mental hospital for 5 years were classified by disorder: schizophrenic, delusional, anxiety, dissociative, and other.

Click or tap here to enter text for question 3.8 e.

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.

Click or tap here to enter text for question 3.8 f.

3.9. A senior psychology major conducted the same experiment three times with groups that consisted of 12, 31, and 17 participants. For the three sessions the mean percent correct was 74, 69, and 75, respectively. What is the mean score of the participants? (LOs: 1)

Click or tap here to enter text for question 3.9.

3.10. a. By inspection, determine the direction of skew of the expenditure data in Table

3.2 and the elevation data in Table 3.4. Verify your judgment by comparing the means and medians. (LOs: 2)

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b. For Problem 2.10 of Chapter 2, you determined by inspection the direction of skew of two distributions (X and Y). To verify your judgment, calculate and compare the mean and median of each distribution. The data are in Problem 2.8 of Chapter 2.

Click or tap here to enter text for question 3.10 b.

3.11. A 3-year veteran of the local baseball team was calculating his lifetime batting average. The first year he played for half the season and batted .350 (28 hits in 80 at-bats). The second year he had about twice the number of at-bats and his average was .325. The third year, although he played even more regularly, he was in a slump and batted only .275. Adding the three season averages and dividing the total by 3, he found his lifetime batting average to be .317. Is this correct? Explain. (LOs: 4)

Click or tap here to enter text for question 3.11.