Therefore, both the median and the mean can go down.

(Even though the group has become economically better off because now these members actually make money.)

With numbers: Assume you have 5 people….. 2 people make no money. One person makes $100,000. One person makes $50,000. And the last person makes $40,000.

The median (not counting the first two people) is just the middle number which is $50,000.

The mean (not counting the first two people) is the average of the three which is $63,333.

****

Now suppose those first two people make money. Now one has $10,000 and the other has $20,000.

The median of the 5 incomes is now $40,000 instead of $50,000.

(Because $40,000 is the middle number between all five incomes.)

The new mean is the new average….. those new incomes of $10,000 and $20,000 push the average down. The new mean is $44,000.

So yes, both the median and the mean can go down.

Edit: Read the question. “omit all members of the group who had no income.” That’s the twist.

So first off, hopefully you know that the mean is the average, the median is the middle number and the mode is the most frequently occurring value. That is just a little review for you to start.

In this problem, we are dealing with median and mean incomes of a group. The “catch” to this question is pretty simple actually. An example would be the following set of data (which we will assume are income values of a group)

11,000 13,000 19,000 21,000 23,000 27,000 35,000

for simplicity sake, we can just express the data without the zeros for now and add them back later:

11, 13, 19, 21, 23, 27, 35

The median of this data is 21 while the mean would be the sum of all the numbers divided by the number of numbers which would be about 21.286

So, say this was 2006’s data. In 2007 there is a financial boom and most people report an increase in income except for one who unfortunately enough lost their job:

11, 14, 20, 22, 0, 29, 36

If we rearrange this data set in numerical order we can find the median a lot easier:

0, 11, 14, 20, 22, 29, 36

Now our median has dropped down to 20 even though most of the incomes have gone up. Now take a look at what happens when you find the mean:

(0+11+14+20+22+29+36)/7=18.857

The mean income has dropped significantly!! The average person that was making $21, 286 per year is now only making $18,857 per year!! Why is this when only one income dropped?

The answer–the mean is heavily influenced by outliers. Outliers in statistics are values that are typically on either end of the range of data, whether that be low or high. These values are the furthest away from the mean and median of the data set.

The median can be somewhat influenced by an outlier as well as we saw, however it is not influenced nearly as much as the mean is.

I hope I answered your question.

71, 75, 75, 80, 85, 89, 91, 94, 99. $85K would be the median income for that group of people.

Now let’s say you take that same nine people a year later, and some of them increased their income and others did not. It might look like this:

72, 75, 76, 80, 84, 90, 92, 94, 99. The median is now 84, but the group as a whole is better off.

This is not true with the mean income. The mean is the mathematical average, so if the group as a whole is better off, then the mean will be higher. It has to be. This is why mean is generally a better central measure than median.