Step by step
The question
Question: Which data set has the bigger standard deviation?
A: 10, 11, 12, 13, 14.
B: 2, 3, 4, 5, 6.
1 Find each mean
The standard deviation, SD, tells how far the numbers usually are from the mean.
So first we need each mean.
A: add them, then divide by how many.
The total is 60.
60 divided by 5 is 12.
Now B: add them, then divide by how many.
The total is 20.
20 divided by 5 is 4.
2 Distances from the mean
Under each number of A, we write how far it is from the mean, 12.
We add the distances: 2 plus 1 plus 0 plus 1 plus 2 is 6.
Now the same for B.
Its mean is 4.
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.
The distances are the same: 6 and 6.
The numbers are just as far from their mean.
The same distances from the mean means the same standard deviation.
Careful!
Bigger numbers do not mean more spread.
The SD only looks at how far each number is from its own mean.
So the two sets have the same standard deviation.
4 Check
Let's check with the range, biggest minus smallest.
A: 4.
B: 4.
The same width too.
So it is right!
Let's look back.
First: find each mean.
Then: distances from the mean.
Then: compare.
Last: check.