Compare 30 (mean 35, sd 5) and 52 (mean 60, sd 4)

Step by step

The question

Question: which is better, 30 in a group with mean 35 and SD 5, or 52 in a group with mean 60 and SD 4?

The groups are different.

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

1 z for 30

Subtract first: 30 minus 35 is −5.

Then −5 divided by 5 is −1.

2 z for 52

52 minus 60 is −8.

Then −8 divided by 4 is −2.

3 Compare

Careful!

52 is the bigger number, but its group is different.

Compare the z-scores.

−1 is more than −2.

So 30 is better, compared with its own group.

4 Check

Let's check each z.

35 plus −1 times 5 is 30.

60 plus −2 times 4 is 52.

So both are right!

Let's look back.

First: z for 30.

Then: z for 52.

Then: compare.

Last: check.