Step by step
The question
Question: Which team is less spread out?
Team A: 12, 15, 18, 21, 24.
Team B: 16, 17, 18, 19, 20.
1 Find each mean
The standard deviation, SD, tells how far the numbers usually are from the mean.
So first we need each mean.
Team A: add them, then divide by how many.
The total is 90.
90 divided by 5 is 18.
Now Team B: add them, then divide by how many.
The total is 90.
90 divided by 5 is 18.
2 Distances from the mean
Under each number of Team A, we write how far it is from the mean, 18.
We add the distances: 6 plus 3 plus 0 plus 3 plus 6 is 18.
Now the same for Team B.
Its mean is 18.
We add the distances: 2 plus 1 plus 0 plus 1 plus 2 is 6.
3 Compare
Both sets have 5 numbers.
So we can just compare the totals.
Team A's numbers are further from the mean, 18 against 6.
Further from the mean means a bigger standard deviation.
We did not work out the SD itself.
But it grows with these distances, so the bigger distance goes with the bigger SD.
Careful!
Both means are the same, but the spread is not.
The SD is about the distances.
So Team B has the smaller standard deviation.
4 Check
Let's check with the range, biggest minus smallest.
Team A: 12.
Team B: 4.
Team A is spread wider too.
So it is right!
Let's look back.
First: find each mean.
Then: distances from the mean.
Then: compare.
Last: check.