Central Tendency and Variability
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
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
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?
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