Here is 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.

(c) If the highest number were decreased to a value smaller 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.

I'm not sure if I did this right but here are my answers:

(a)Both the mean and median would increase.
(b)Both the mean and median would decrease.
(c) Both the mean and median would decrease.

Can anyone check to see what I did wrong?

The median is essentially the 50th percentile.

Think of the mean as a fulcrum or balance point.

a) disagree

b) disagree

c) agree

I fixed my answer but I'm not sure if it is right...

a)The mean would increase while the median would remain the same.

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

(b) the mean would decrease while the median remained the same

Based on your answers, it seems that you have correctly interpreted the effects of changing the highest number on the median and mean. Here is the breakdown of each scenario:

(a) If the highest number were increased, the mean would remain the same while the median would increase. This is because the mean is influenced by all the values in the dataset, so increasing the highest number would have no impact on its calculation. However, the median represents the middle value when the data is arranged in ascending order, so adding a higher number would shift the middle value higher, resulting in an increase in the median.

(b) If the highest number were decreased to a value still larger than B, both the mean and median would decrease. Decreasing the highest number in the dataset would reduce the overall value sum, leading to a lower mean. Additionally, as the median represents the middle value, removing a higher number would lower the middle value, resulting in a decrease in the median as well.

(c) If the highest number were decreased to a value smaller than B, both the mean and median would decrease. Similar to scenario (b), decreasing the highest number in the dataset would diminish the overall value sum, leading to a lower mean. Additionally, since the highest number is smaller than the median, removing it would shift the middle value lower, causing a decrease in the median too.

Therefore, your answers are correct:

(a) Both the mean and median would increase.
(b) Both the mean and median would decrease.
(c) Both the mean and median would decrease.