Data: 3, 9, 4, 8, 6. Add 30. What happens to the mean and the median?

Step by step

The question

Question: Data: 3, 9, 4, 8, 6.

Add 30.

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, we put the numbers in order, 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

30 comes in, so the total gets 30 more.

30 plus 30 is 60.

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: 60 divided by 6.

So the new mean is 10.

4 Median after

Now 30 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 10.

10 minus 6 is 4.

So it went up 4.

The median went up from 6 to 7.

7 minus 6 is 1.

So it went up 1.

30 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 4, and the median goes up 1.

6 Check

Let's check the new mean: if every number were 10, 6 of them would make 10 times 6.

That is 60, 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.