Step by step
The question
Question: Data: 0, 10, 11, 12, 12.
Remove 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 45.
There are 5 numbers.
The mean shares the total equally: 45 divided by 5.
So the mean is 9.
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.
11 is left in the middle.
So the median is 11.
3 Mean after
0 is gone, so the total loses 0.
45 minus 0 is 45.
One number less: now there are 4.
Careful!
We have 4 numbers now, not 5.
So we share by 4.
We share the new total equally: 45 divided by 4.
45 does not share out evenly.
4 times 11 is 44.
1 is left, and 1 divided by 4 is 0.25.
So the new mean is 11.25.
4 Median after
Now the list in order, without 0.
We cross out the smallest and the biggest, one pair at a time.
Two numbers are left in the middle: 11 and 12.
The median is halfway between them: we add them and divide by 2.
11 plus 12 is 23.
23 divided by 2 is 11.5.
5 Compare
The mean went up from 9 to 11.25.
11.25 minus 9 is 2.25.
So it went up 2.25.
The median went up from 11 to 11.5.
11.5 minus 11 is 0.5.
So it went up 0.5.
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 up 2.25, and the median goes up 0.5.
6 Check
Let's check the new mean: if every number were 11.25, 4 of them would make 11.25 times 4.
That is 45, 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.