Step by step
The question
Question: Data: 10, 12, 13, 15, 50.
Remove 50.
What happens to the mean and the median?
1 Mean before
We add all the numbers, from left to right.
So the total is 100.
There are 5 numbers.
The mean shares the total equally: 100 divided by 5.
So the mean is 20.
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.
13 is left in the middle.
So the median is 13.
3 Mean after
50 is gone, so the total loses 50.
100 minus 50 is 50.
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: 50 divided by 4.
50 does not share out evenly.
4 times 12 is 48.
2 is left, and 2 divided by 4 is 0.5.
So the new mean is 12.5.
4 Median after
Now the list in order, without 50.
We cross out the smallest and the biggest, one pair at a time.
Two numbers are left in the middle: 12 and 13.
The median is halfway between them: we add them and divide by 2.
12 plus 13 is 25.
25 divided by 2 is 12.5.
5 Compare
The mean went down from 20 to 12.5.
20 minus 12.5 is 7.5.
So it went down 7.5.
The median went down from 13 to 12.5.
13 minus 12.5 is 0.5.
So it went down 0.5.
50 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 7.5, and the median goes down 0.5.
6 Check
Let's check the new mean: if every number were 12.5, 4 of them would make 12.5 times 4.
That is 50, 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.