# Statistics for the Behavioral Sciences

On a separate piece of paper, show all of your work and be neat.

1. What is the difference between ΣX2 and (ΣX) 2?

2. What is the symbol for the mean of the population? What is the symbol for

the mean of a sample? What is the symbol for the standard deviation of the

population? What is the symbol for the standard deviation of a sample?

3. What measure of central tendency is appropriate for qualitative data?

4. If the mean is larger than the median, the distribution will be __________

skewed, but if the median is larger than the mean, the distribution will be

__________ skewed. Similar values of the mode, median, and mean indicate

that the distribution is __________.

5. Ten preschool children on a playground were asked to guess their mother’s

age. Calculate the mean, median, and mode of their guesses.

39, 19, 34, 57, 100, 7, 44, 18, 25, 19

6. Two salesmen working for the same company are having an argument. Each

claims that the average price of items he sold, averaged over the last month, was

the highest in the company. Can they both be right? Explain.

7. In what circumstance would you choose to use the interquartile range, rather

than the range?

8. Describe in words the relationship between the variance and the standard

deviation. Describe in symbols the relationship between the variance and the

standard deviation.

9. Why do we use (n – 1) in the denominator for calculating the standard

deviation of a sample, but use (N) in the denominator for calculating the standard

deviation of a population?

10. If s = 0, what must be true about the scores in the distribution?

11. Compute the standard deviation of the following population, once using the

definitional formula, and again using the computational formula.

7, 9, 0, 1, 7, 4, 4, 7, 6

12. Compute the mean and standard deviation of the following sample of scores:

22, 45, 34, 25, 23, 36, 23, 38, 27, 32, 44, 55

After rounding your answers off to the nearest whole number, answer the

following questions:

a) What score would be two standard deviations below the mean?

b) What score would be one standard deviation above the mean?

13. Two statistics classes have taken their first exam, and both classes scored a

mean of 75. In Tuesday’s class, the standard deviation was 5 points, and in

Thursday’s class the standard deviation was 10 points. If your grade were 70,

which class would you rather be in? If your grade were 85, which class would

you rather be in? Does the standard deviation make a difference in your answer

even though the two class means were the same? Why?