Compare 88 (mean 80, sd 4) and 75 (mean 65, sd 8)

Step by step

The question

Question: which is better, 88 in a group with mean 80 and SD 4, or 75 in a group with mean 65 and SD 8?

The groups are different.

So we compare z-scores: how many SDs each is above its own mean.

1 z for 88

Subtract first: 88 minus 80 is 8.

Then 8 divided by 4 is 2.

2 z for 75

75 minus 65 is 10.

Then 10 divided by 8 is 1.25.

3 Compare

Careful!

The groups are different.

So we compare the z-scores, not the numbers.

2 is more than 1.25.

So 88 is better, compared with its own group.

4 Check

Let's check each z.

80 plus 2 times 4 is 88.

65 plus 1.25 times 8 is 75.

So both are right!

Let's look back.

First: z for 88.

Then: z for 75.

Then: compare.

Last: check.