Which data set has the bigger standard deviation? A: 10, 20, 30. B… Step by Step

Step by step

The question

Question: Which data set has the bigger standard deviation?

A: 10, 20, 30.

B: 18, 20, 22.

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 3 is 20.

mean of A = 10 + 20 + 303 = 603 = 20

SD = how far the numbers usually are from the mean

Now B: add them, then divide by how many.

The total is 60.

60 divided by 3 is 20.

mean of B = 18 + 20 + 223 = 603 = 20

2 Distances from the mean

Under each number of A, we write how far it is from the mean, 20.

A : 10, 20, 30

how far = bigger − smaller

We add the distances: 10 plus 0 plus 10 is 20.

A total = 10 + 0 + 10 = 20

Now the same for B.

Its mean is 20.

B : 18, 20, 22

We add the distances: 2 plus 0 plus 2 is 4.

B total = 2 + 0 + 2 = 4

3 Compare

Both sets have 3 numbers.

So we can just compare the totals.

3 numbers in each: compare the totals

A's numbers are further from the mean, 20 against 4.

= A: 20 > B: 4

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.

= further from the mean → bigger SD

Careful!

Both means are the same, but the spread is not.

The SD is about the distances.

Careful: not same mean → same SD ✗

So A has the bigger standard deviation.

= A has the bigger SD

4 Check

Let's check with the range, biggest minus smallest.

A: 20.

B: 4.

A is spread wider too.

So it is right!

range A: 30 − 10 = 20, B: 22 − 18 = 4

Let's look back.

First: find each mean.

Then: distances from the mean.

Then: compare.

Last: check.

Answer