(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 greater 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 the most sensitive to extreme values or outliers. Adding a significantly higher salary increases 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 tail is on the left, pulling the mean down. (iii) In a positively skewed distribution, the mode is less than the median, which is consistent with the statement as the tail is on the right, indicating that the median is greater than the mode.

(I a Small Manufacturing Company with 52 Employees Has Annual