Which data set has the bigger standard deviation? A: 10, 20, 30, 40… Step by Step

Step by step

The question

Question: Which data set has the bigger standard deviation?

A: 10, 20, 30, 40, 50.

B: 100, 200, 300, 400, 500.

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 150.

150 divided by 5 is 30.

mean of A = 10 + 20 + 30 + 40 + 505 = 1505 = 30

SD = how far the numbers usually are from the mean

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

The total is 1500.

1500 divided by 5 is 300.

mean of B = 100 + 200 + 300 + 400 + 5005 = 15005 = 300

2 Distances from the mean

Under each number of A, we write how far it is from the mean, 30.

A : 10, 20, 30, 40, 50

how far = bigger − smaller

We add the distances: 20 plus 10 plus 0 plus 10 plus 20 is 60.

A total = 20 + 10 + 0 + 10 + 20 = 60

Now the same for B.

Its mean is 300.

B : 100, 200, 300, 400, 500

We add the distances: 200 plus 100 plus 0 plus 100 plus 200 is 600.

B total = 200 + 100 + 0 + 100 + 200 = 600

3 Compare

Both sets have 5 numbers.

So we can just compare the totals.

5 numbers in each: compare the totals

B's numbers are further from the mean, 600 against 60.

= A: 60 < B: 600

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

So B has the bigger standard deviation.

= B has the bigger SD

4 Check

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

A: 40.

B: 400.

B is spread wider too.

So it is right!

range A: 50 − 10 = 40, B: 500 − 100 = 400

Let's look back.

First: find each mean.

Then: distances from the mean.

Then: compare.

Last: check.

Answer