What is the median of 12, 7, 15, 9, 20, 11?

Step by step

The question

Question: find the median of 12, 7, 15, 9, 20 and 11.

The median is the middle number, once the numbers are in order.

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Put them in order

First we put them in order, smallest first: 7, 9, 11, 12, 15 and 20.

We still have 6 numbers.

None is lost.

2 Find the middle

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

And the next pair.

Two numbers are left in the middle: 11 and 12.

The median is halfway between them.

Halfway: we add them and divide by 2.

11 plus 12 is 23.

23 divided by 2 is 11.5.

So the median is 11.5.

3 Pick the choice

Our answer is median = 11.5.

That is choice A.

4 Why not the others

B is 12.

Wrong: halfway between 15 and 9: the middle of the list before it was put in order.

C is 12.33.

Wrong: that is the mean.

D is 13.5.

Wrong: halfway between the smallest and the biggest.

Let's look back.

First: put them in order.

Then: find the middle.

Then: pick the choice.

Last: why not the others.