Which store is more spread out? Store A: 4, 6, 8, 10. Store B: 1, 7… Step by Step

Step by step

The question

Question: Which store is more spread out?

Store A: 4, 6, 8, 10.

Store B: 1, 7, 7, 13.

1 Find each mean

The standard deviation, SD, tells how far the numbers usually are from the mean.

So first we need each mean.

Store A: add them, then divide by how many.

The total is 28.

28 divided by 4 is 7.

mean of Store A = 4 + 6 + 8 + 104 = 284 = 7

SD = how far the numbers usually are from the mean

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

The total is 28.

28 divided by 4 is 7.

mean of Store B = 1 + 7 + 7 + 134 = 284 = 7

2 Distances from the mean

Under each number of Store A, we write how far it is from the mean, 7.

Store A : 4, 6, 8, 10

how far = bigger − smaller

We add the distances: 3 plus 1 plus 1 plus 3 is 8.

Store A total = 3 + 1 + 1 + 3 = 8

Now the same for Store B.

Its mean is 7.

Store B : 1, 7, 7, 13

We add the distances: 6 plus 0 plus 0 plus 6 is 12.

Store B total = 6 + 0 + 0 + 6 = 12

3 Compare

Both sets have 4 numbers.

So we can just compare the totals.

4 numbers in each: compare the totals

Store B's numbers are further from the mean, 12 against 8.

= Store A: 8 < Store B: 12

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 Store B has the bigger standard deviation.

= Store B has the bigger SD

4 Check

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

Store A: 6.

Store B: 12.

Store B is spread wider too.

So it is right!

range Store A: 10 − 4 = 6, Store B: 13 − 1 = 12

Let's look back.

First: find each mean.

Then: distances from the mean.

Then: compare.

Last: check.

Answer