1. In words, explain what is measured by each of the following: a. SS b. Variance c. Standard deviation

2. Can SS ever have a value less than zero? Explain your answer.

6. A population has a mean of m 5 80 and a standard deviation of s 5 20. a. Would a score of X 5 70 be considered an extreme value (out in the tail) in this sample? b. If the standard deviation were s 5 5, would a score of X 5 70 be considered an extreme value?

8. Calculate the mean and SS (sum of squared deviations) for each of the following samples. Based on the value for the mean, you should be able to decide which SS formula is better to use. Sample A: 1 4 8 5 Sample B: 3 0 9 4

10. For the following sample of n 5 7 scores: 8 6 5 2 6 3 5

c. Compute SS, variance, and standard deviation for the sample. (How well does your estimate compare with the actual value of s?)

13. A population has a mean of m 5 30 and a standard deviation of s 5 5. a. If 5 points were added to every score in the population, what would be the new values for the mean and standard deviation? b. If every score in the population were multiplied by 3, what would be the new values for the mean and standard deviation?

22. In an extensive study involving thousands of British children, Arden and Plomin (2006) found significantly higher variance in the intelligence scores for males than for females. Following are hypothetical data, similar to the results obtained in the study. Note that the scores are not regular IQ scores but have been standardized so that the entire sample has a mean of M 5 10 and a standard deviation of s 5 2. a. Calculate the mean and the standard deviation for the sample of n 5 8 females and for the sample of n 5 8 males. b. Based on the means and the standard deviations, describe the differences in intelligence scores for males and females. Female9,11,10,13,8,9,11,9 Male 8,10,11,12,6,10,14,9

23. Within a population, the differences that exist from one person to another are often called diversity. Researchers comparing cognitive skills for younger

adults and older adults, typically find greater differences (greater diversity) in the older population (Morse, 1993). Following are typical data showing problem-solving scores for two groups of participants.

Older Adults (average age 72) Younger Adults (average age 31)

9 4 7 3 8 7 9 6 7 8

6 2 8 4 5 6 7 6 6 8

7 5 2 6 6 9 7 8 6 9

a. Compute the mean, the variance, and the standard deviation for each group.

b. Is one group of scores noticeably more variable (more diverse) than the other?

HW #3 – Part 2

Question 1

Find the mode for the following variables

17,1, 5, 5, 17, 17,2, 9, 6, 9,17,17

Question 2

Find the mode for the following variables

2,12, 2, 9, 2,12, 10, 2, 6,12,12

Question 3

Find the median for the following variables

19,3, 8, 14, 19, 19,22, 29, 32, 3,19,19

Question 4

Find the median for the following variables

20,1, 9, 13, 20, 20,23, 30, 35, 37,20

Question 5

Find the mean (average) for the following set of numbers:

x = 3, 6, 14, 3, 5, 9, 10, 16, 11, 9

Be sure to round your answer to the nearest 2 decimal places.

Question 6

Find the mean (average) for the following set of numbers:

x = 11, 22, 12, 24, 12, 6, 10, 9, 9, 7

Be sure to round your answer to the nearest 2 decimal places.

Question 7

Calculate the range for the following variables

2, 8, 10, 9, 4, 6, 9, 14

Question 8

Calculate the range for the following variables

3, 24, 20, 21, 33, 24, 16, 23`

Question 9

Find the population standard deviation for the following values:

Be sure to round your answer to the 2 nearest decimal places.

2, 9, 2, 10, 1

Question 10

Find the population standard deviation for the following values:

Be sure to round your answer to the 2 nearest decimal places.

42, 14, 41, 31, 8

SAMPLE ASSIGNMENT

Sample-2