Chapter 4, Problem 25E

(a)

To determine

To Explain: the median and mean.

Answer to Problem 25E

Median would be affected marginally.

The mean would be skewed upward.

Explanation of Solution

Median would be affected marginally.

The mean would be skewed upward.

The median would be, at most, shifted over one value either above, below, or not at all. If assume that the researcher’s salary is the highest, it would have no impact on the median. The largest number was already the largest number, and was not counted in the median anyway, as it cannot be the centre data point. The, mean; however is the average of all values. Replacing one value with a much larger value would cause the mean to increase.

(b)

To determine

To Explain: the range IQR and standard deviation.

Answer to Problem 25E

The range would be increase significantly.

The IQR would not be change.

The standard deviation would increase significantly.

Explanation of Solution

Assuming the researcher’s salary is the highest in the company:

The range would be increase significantly (by 1.8 million, to be exact).

The IQR would not be change.

The standard deviation would increase significantly.

The range is the highest number minus the lowest, if the highest increases significantly, the range would increase by the change. The IQR only counts the first and third quartile values, which are found similarly to the median (by discounting endpoints and only counting the middle data point). The boss salary was already the largest; making it larger will not affect the IQR. The standard deviation would increase significantly, as the increasing the value of a data point would increase the overall spread.