(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, 90 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) When the mean is smaller than the median and mode, it indicates a negatively skewed distribution, hence Pearson's coefficient of skewness would be negative. (ii) Variance equals the square of the standard deviation, so they are only equal when both are 1. (iii) According to the Empirical Rule, about 68% of observations lie within one standard deviation of the mean, not 90%.

(I If the Mean of a Frequency Distribution Is Smaller