Step by step
The question
Question: Data: 8, 9, 10, 11, 12, 10.
Add 80.
What happens to the mean and the median?
1 Mean before
We add all the numbers, from left to right.
So the total is 60.
There are 6 numbers.
The mean shares the total equally: 60 divided by 6.
So the mean is 10.
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.
Two numbers are left in the middle: 10 and 10.
The median is halfway between them: we add them and divide by 2.
10 plus 10 is 20.
20 divided by 2 is 10.
3 Mean after
80 comes in, so the total gets 80 more.
60 plus 80 is 140.
One more number: now there are 7.
Careful!
We have 7 numbers now, not 6.
So we share by 7.
We share the new total equally: 140 divided by 7.
So the new mean is 20.
4 Median after
Now 80 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.
10 is left in the middle.
So the new median is 10.
5 Compare
The mean went up from 10 to 20.
20 minus 10 is 10.
So it went up 10.
The median was 10, and it is still 10.
It stays the same.
80 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 10, and the median stays the same.
6 Check
Let's check the new mean: if every number were 20, 7 of them would make 20 times 7.
That is 140, 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.