Step by step
The question
Question: Data: 20, 21, 22, 23, 24, 100.
Remove 100.
What happens to the mean and the median?
1 Mean before
We add all the numbers, from left to right.
So the total is 210.
There are 6 numbers.
The mean shares the total equally: 210 divided by 6.
So the mean is 35.
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.
Two numbers are left in the middle: 22 and 23.
The median is halfway between them: we add them and divide by 2.
22 plus 23 is 45.
45 divided by 2 is 22.5.
3 Mean after
100 is gone, so the total loses 100.
210 minus 100 is 110.
One number less: now there are 5.
Careful!
We have 5 numbers now, not 6.
So we share by 5.
We share the new total equally: 110 divided by 5.
So the new mean is 22.
4 Median after
Now the list in order, without 100.
We cross out the smallest and the biggest, one pair at a time.
And the next pair.
22 is left in the middle.
So the new median is 22.
5 Compare
The mean went down from 35 to 22.
35 minus 22 is 13.
So it went down 13.
The median went down from 22.5 to 22.
22.5 minus 22 is 0.5.
So it went down 0.5.
100 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 13, and the median goes down 0.5.
6 Check
Let's check the new mean: if every number were 22, 5 of them would make 22 times 5.
That is 110, 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.