(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, 99 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

- Statement (i) is correct because when the mean is less than the median and mode, it indicates a negatively skewed distribution, hence Pearson's coefficient of skewness would be negative.- Statement (ii) is correct because variance equals the square of the standard deviation, so they only equal when both are 1 (since 1 squared is still 1).- Statement (iii) is incorrect because according to the Empirical Rule, 68% of observations lie within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

(I If the Mean of a Frequency Distribution Is Smaller