Question

If 10 is added to the maximum value and 10 is subtracted from the minimum value of a set of ages of citizens waiting in line to vote, which of the following is true? a-The mean age and median age are unchanged. b-The mean age changes but the median age does not change. c- The median age changes but the mean age does not change. d-The effect on the mean and median cannot be determined without knowing the other ages. e-None of these.

Answer 1

a-The mean age and median age are unchanged.

Explanation:

By adding the same you are subtracting, the sum of the ages remains the same. Therefore, the mean remains the same since you are dividing the same total of ages by the same number of people.

The middle number continues to be the middle number, so the median also does not change.

Try an example.

The ages are 30, 40, 50, 60, 70

Mean = (30 + 40 + 50 + 60 + 70)/5 = 250/5 = 50

Median: 50

Now add 10 to the greatest value and subtract 10 from the least value.

The ages now are 20, 40, 50, 60, 80

Mean = (20 + 40 + 50 + 60 + 80)/5 = 250/5 = 50

Median: 50

As you can see, both the mean and the median did not change.

Answer: a-The mean age and median age are unchanged.

Answer 2

The mean age and median age are unchanged

Explanation:

The median will not change when we alter the lowest and highest values so we can eliminate the answers that say the median changes

The mean is found by adding the values together and dividing by the number of values

If we add 10 and subtract 10, we have not changed the total value before dividing, so the mean does not change