(i. A small manufacturing company with 52 employees has annual salaries distributed such that the mean is $25,459, the median is $24,798 and the mode is $24,000. An additional foreman is hired at an annual salary of $50,700. The measure of central tendency that is most affected by the addition of this salary is the arithmetic mean. (ii) In the relationship between the mean and median in a negatively skewed distribution the mean is less than the median.
(iii) In the relationship between the median and the mode in a positively skewed distribution, the median is smaller than the mode.
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) The arithmetic mean is sensitive to extreme values, so adding a significantly higher salary will increase the mean more than it would affect the median or mode. (ii) In a negatively skewed distribution, the mean is indeed less than the median because the lower values drag the mean down. (iii) However, in a positively skewed distribution, the median is greater than the mode, not smaller, because the long tail to the right pulls the mean above the median, and the median is typically above the mode.

(I a Small Manufacturing Company with 52 Employees Has Annual