# Math

1. Given two samples, one in which n = 36, the other where n = 60, which distribution would have the larger variance? Which variance is likely to be closer in value to the population variance? Which sample is likely to have the larger range?

2. A school psychologist wants to inform a teacher about the mean and standard deviation of the students IQ scores. The scores are below; assume they are a sample.

IQ scores 98, 111, 102, 100,101,109

A. What is the mean?

B. What is the standard deviation?

3. Calculate the range, variance, and standard deviation of this sample of scores.

A. 2, 4, 7, 4, 8, 5, 1, 4, 4, 5

B. What is the range?

C. What is the variance?

D. What is the standard deviation?

4. For the following populations of scores, find the mean deviations:

A. 5, 7, 9, 9, 13, 14, 15, 16

B. 23, 25, 31, 34, 36, 39, 44, 56, 63, 69

C. 6, 8, 3, 9, 1, 4, 7, 4, 1, 1, 8, 2

5. What does a distribution with a mean of 50 and standard deviation of zero look like?

6. Calculate the variance and standard deviation for this population of scores.

Which for this population of scores.

22,32,32,21,20,19,15,23

7. Which distribution of sample scores has the larger variance?

A. Distribution A : 2, 4, 5, 1, 1, 2, 3, 9

B. Distribution B : 34, 39, 34, 35, 33, 32

8. A negatively skewed distribution has a mean of 500 and a standard deviation of 100. Given what we have learned in this chapter, is it possible to determine the percentage of scores that fall between 400 and 600? If so, what is

9. If a normal distribution has a mean of 50 and a standard deviation of 10, what scores encapsulate the middle 68% of the distribution? The middle 95% of the distribution? The middle 99.7% of the distribution?

10. What if a normal distribution has the same mean as in question 17, but had a standard deviation of 2. What scores would encapsulate the middle 68, 95, and 99.7% of scores?

11. If a normal distribution has a variance of 100 and 95% of the scores are between the values of 120 and 160 what is the mean?

12.

Determine the mean variance standard deviation and range for each of the following sample distributions

3 5 3 7 9 10 2 12 15

1 8 9 6 4 11 1 11 10

1 4 5 5 3 10 9 13 14

102 100 99 81 75 113 100

106 114 82 79 88 111 104

100 106 85 99 82 101 100