Which class is more spread out? Class 1: 70, 75, 80. Class 2: 60… Step by Step

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The question

Question: Which class is more spread out?

Class 1: 70, 75, 80.

Class 2: 60, 75, 90.

1 Find each mean

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

So first we need each mean.

Class 1: add them, then divide by how many.

The total is 225.

225 divided by 3 is 75.

mean of Class 1 = 70 + 75 + 803 = 2253 = 75

SD = how far the numbers usually are from the mean

Now Class 2: add them, then divide by how many.

The total is 225.

225 divided by 3 is 75.

mean of Class 2 = 60 + 75 + 903 = 2253 = 75

2 Distances from the mean

Under each number of Class 1, we write how far it is from the mean, 75.

Class 1 : 70, 75, 80

how far = bigger − smaller

We add the distances: 5 plus 0 plus 5 is 10.

Class 1 total = 5 + 0 + 5 = 10

Now the same for Class 2.

Its mean is 75.

Class 2 : 60, 75, 90

We add the distances: 15 plus 0 plus 15 is 30.

Class 2 total = 15 + 0 + 15 = 30

3 Compare

Both sets have 3 numbers.

So we can just compare the totals.

3 numbers in each: compare the totals

Class 2's numbers are further from the mean, 30 against 10.

= Class 1: 10 < Class 2: 30

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 Class 2 has the bigger standard deviation.

= Class 2 has the bigger SD

4 Check

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

Class 1: 10.

Class 2: 30.

Class 2 is spread wider too.

So it is right!

range Class 1: 80 − 70 = 10, Class 2: 90 − 60 = 30

Let's look back.

First: find each mean.

Then: distances from the mean.

Then: compare.

Last: check.

Answer