(i. If the mean of a frequency distribution is smaller than the median and mode, the Pearson's coefficient of skewness would be negative. (ii) The only time the variance equals the standard deviation is when both equal 1.
(iii) According to the Empirical Rule, 68 percent of the observations lie within plus and minus one standard deviation of the mean.
A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements, but not (i).
E) (i), (ii) and (iii) are all false statements.

Question

Quizplus · Accepted Answer

(i) is correct because if the mean is smaller than the median and mode, the distribution is negatively skewed. (ii) is incorrect because the variance can equal the standard deviation when both are 0. (iii) is correct because the Empirical Rule states that 68% of the observations lie within one standard deviation of the mean.

(I If the Mean of a Frequency Distribution Is Smaller