PSY 216
Assignment 4 Answers
1. Problem 2 from the text
Can SS ever have a value less than zero? Explain your answer.
SS = Σ(X - )2. When you square a real number, the result is always non-negative. The sum of non-negative
numbers must be non-negative.
2. Problem 4 from the text
What does it mean for a sample to have a standard deviation of zero? Describe the scores in such a sample.
If the standard deviation is 0 then the variance is 0 and the mean of the squared deviation scores must be 0.
The sum of the squared deviation scores must be equal to 0 for the mean of the squared deviation scores to be
equal to 0. Since the squared deviation scores must be non-negative because they are squared, all of the
squared deviation scores must be 0; otherwise, the sum would be non-zero. The only way that each squared
deviation score can be equal to 0 is if all of the scores equal the mean. Thus, when the standard deviation
equals 0, all the scores are identical and equal to the mean.
3. Problem 5 from the text
Explain why the formulas for sample variance and population variance are different.
The extreme scores in a population that is approximately normal in shape are less likely to be
included in a sample because of their rarity. Thus, the sample is usually less variable than the
population. By dividing the sum of squares of the sample by a slightly smaller number (n – 1 instead
of n), the variance will be slightly larger, correcting for underestimation.
4. Problem 7 from the text
On an exam with a mean of M = 78, you obtain a score of X = 84.
a. Would you prefer a standard deviation of s = 2 or s = 10? (Hint: Sketch each distribution
and find the location of your score.)
One should prefer s = 2 as a score of 84 is an extremely large value in such a distribution.
You likely did much better than everyone else. With s = 10, your score is less extreme and
others likely did better than you.
b. If your score was X = 72, would you prefer s = 2 or s = 10. Explain your answer.
One should prefer s = 10 as your below average performance is not an extreme score. With
