The question:Consider a data set of 15 distinct measurements with mean A and median B.

(a) If the highest number were increased, what would be the effect on the median and mean? Explain.

The mean would remain the same while the median would increase.
Both the mean and median would increase.
Both the mean and median would remain the same.
The mean would increase while the median would remain the same.

(b) If the highest number were decreased to a value still larger than B, what would be the effect on the median and mean?

The mean would decrease while the median would remain the same.
Both the mean and median would decrease.
Both the mean and median would remain the same.
The mean would remain the same while the median would decrease.

My answers:

a)Both the mean and median would remain the same.

b)The mean would decrease while the median would remain the same.

The mean is a fulcrum (balance point) for the distribution.

The median is the 50th percentile.

a) disagree

b) agree

Your answers are incorrect. Let me explain.

(a) If the highest number in the data set is increased, it would impact both the median and mean.

First, let's talk about the median. The median is the middle value when the data set is arranged in ascending or descending order. Since the data set has 15 distinct measurements, the median is the 8th value (in ascending order). If we increase the highest number, it would not affect the position of the 8th value. Therefore, the median would remain the same.

Now, let's consider the mean. The mean is calculated by summing up all the values in the data set and dividing by the total number of values. Since we are only increasing the highest number, it would not impact the sum of all the numbers. Therefore, the mean would also remain the same.

Thus, the correct answer is: Both the mean and median would remain the same.

(b) If the highest number is decreased to a value still larger than B, it would also impact the mean and median.

The median remains unaffected because it is the middle value when the data set is arranged in ascending or descending order. Therefore, decreasing the highest number would not change the position of the middle value.

However, the mean would be affected. Since the mean is calculated by dividing the sum of all the values by the total number of values, decreasing the highest number would reduce the sum of the values. Consequently, the mean would decrease as well.

Thus, the correct answer is: The mean would decrease while the median would remain the same.