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.

I'm not sure if my answer is right... can someone check for me?

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

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

No and no.

Hope this helps

There would still be the same number of values on either side of the median, so it would be unchanged. The sum of the values would decrease, so the mean would also decrease.
(b)2. The count of values greater than the existing median would decrease and the count below the existing median would increase. The value of the median would have to decrease to restore the equality of the count. The sum of the values would decease which would decrease the mean value..

Thank you for helping!

So for part:

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

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

To answer the question, let's understand the concepts of mean and median and how they are affected by changes in the data.

Mean: The mean is the average of the data set and is calculated by summing up all the values and dividing by the number of values. It is sensitive to extreme values in the data set.

Median: The median is the middle value of an ordered data set. If the data set has an odd number of observations, the median is the middle value. If the data set has an even number of observations, the median is the average of the two middle values. The median is less sensitive to extreme values.

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

In this case, the highest number is increased. Since the mean is calculated by finding the average of all the numbers in the data set, adding a higher value will increase the sum of all the numbers. As a result, the mean will increase.

However, the median is not affected by the magnitude of the highest number. As long as the highest number remains greater than all other values, the position of the median will not change. Therefore, the median will remain the same.

So, the correct answer for part (a) is: 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?

In this case, the highest number is decreased. Since the mean is calculated by summing up all the values and dividing by the number of values, reducing the highest number will decrease the sum of all the numbers. As a result, the mean will decrease.

Similar to part (a), the median is not affected by the absolute magnitude of the highest number. As long as the highest number remains greater than all other values, the position of the median will not change. Therefore, the median will remain the same.

So, the correct answer for part (b) is: Both the mean and median would remain the same.

It seems your initial answers were correct.