Scores: 60, 70, 80, 90. Add 0. What happens to the mean and the…

Step by step

The question

Question: Scores: 60, 70, 80, 90.

Add 0.

What happens to the mean and the median?

1 Mean before

We add all the numbers, from left to right.

So the total is 300.

There are 4 numbers.

The mean shares the total equally: 300 divided by 4.

So the mean is 75.

2 Median before

The median is the middle number.

For it, the numbers must be in order.

They already are, smallest first.

We cross out the smallest and the biggest, one pair at a time.

Two numbers are left in the middle: 70 and 80.

The median is halfway between them: we add them and divide by 2.

70 plus 80 is 150.

150 divided by 2 is 75.

3 Mean after

0 comes in, so the total gets 0 more.

300 plus 0 is 300.

One more number: now there are 5.

Careful!

We have 5 numbers now, not 4.

So we share by 5.

We share the new total equally: 300 divided by 5.

So the new mean is 60.

4 Median after

Now 0 goes into the list, in its place in order.

We cross out the smallest and the biggest, one pair at a time.

And the next pair.

70 is left in the middle.

So the new median is 70.

5 Compare

The mean went down from 75 to 60.

75 minus 60 is 15.

So it went down 15.

The median went down from 75 to 70.

75 minus 70 is 5.

So it went down 5.

0 is far from the other numbers.

A far number pulls the mean a lot.

Only the middle numbers matter for the median.

So the far number does not pull it, and it moves just a little.

So the mean goes down 15, and the median goes down 5.

6 Check

Let's check the new mean: if every number were 60, 5 of them would make 60 times 5.

That is 300, the new total.

So it is right!

Let's look back.

First: mean before.

Then: median before.

Then: mean after.

Then: median after.

Then: compare.

Last: check.