i. In a positively skewed distribution, the mean is always greater than the median. ii. In a negatively skewed distribution, the median occurs at the peak of the curve.
iii. In a negatively skewed distribution, the mode is greater than the median.
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) (i) is a correct statement, but not (ii) or (iii).
E) (i), (ii) and (iii) are all false statements.

Question

Quizplus · Accepted Answer

Statement (i) is always true for positively skewed distributions because the long tail towards the right pulls the mean in that direction, making it greater than the median.
Statement (ii) is not always true. The median does not necessarily occur at the peak of the curve; it merely divides the area under the curve into two equal halves, including the area of any tails. However, in a negatively skewed distribution, the median would be closer to the higher values because the tail of the curve is longer on the left, so it would still be considered "at the left side of the peak."
Statement (iii) is incorrect because in a negatively skewed distribution, the mode is usually less than the median as the tail of the distribution is too spread out.

I in a Positively Skewed Distribution, the Mean Is Always