Which data set has the bigger standard deviation? A: 1, 5, 9. B: 4… Step by Step

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The question

Question: Which data set has the bigger standard deviation?

A: 1, 5, 9.

B: 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 15.

15 divided by 3 is 5.

mean of A = 1 + 5 + 93 = 153 = 5

SD = how far the numbers usually are from the mean

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

The total is 15.

15 divided by 3 is 5.

mean of B = 4 + 5 + 63 = 153 = 5

2 Distances from the mean

Under each number of A, we write how far it is from the mean, 5.

A : 1, 5, 9

how far = bigger − smaller

We add the distances: 4 plus 0 plus 4 is 8.

A total = 4 + 0 + 4 = 8

Now the same for B.

Its mean is 5.

B : 4, 5, 6

We add the distances: 1 plus 0 plus 1 is 2.

B total = 1 + 0 + 1 = 2

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, 8 against 2.

= A: 8 > B: 2

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: 8.

B: 2.

A is spread wider too.

So it is right!

range A: 9 − 1 = 8, B: 6 − 4 = 2

Let's look back.

First: find each mean.

Then: distances from the mean.

Then: compare.

Last: check.

Answer