Data: 3, 5, 6, 8, 8. Add 36. What happens to the mean and the median?

Step by step

The question

Question: Data: 3, 5, 6, 8, 8.

Add 36.

What happens to the mean and the median?

1 Mean before

We add all the numbers, from left to right.

So the total is 30.

There are 5 numbers.

The mean shares the total equally: 30 divided by 5.

So the mean is 6.

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.

And the next pair.

6 is left in the middle.

So the median is 6.

3 Mean after

36 comes in, so the total gets 36 more.

30 plus 36 is 66.

One more number: now there are 6.

Careful!

We have 6 numbers now, not 5.

So we share by 6.

We share the new total equally: 66 divided by 6.

So the new mean is 11.

4 Median after

Now 36 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.

Two numbers are left in the middle: 6 and 8.

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

6 plus 8 is 14.

14 divided by 2 is 7.

5 Compare

The mean went up from 6 to 11.

11 minus 6 is 5.

So it went up 5.

The median went up from 6 to 7.

7 minus 6 is 1.

So it went up 1.

36 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 up 5, and the median goes up 1.

6 Check

Let's check the new mean: if every number were 11, 6 of them would make 11 times 6.

That is 66, 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.