Compare 65 (mean 60, sd 10) and 58 (mean 50, sd 4)

Step by step

The question

Question: which is better, 65 in a group with mean 60 and SD 10, or 58 in a group with mean 50 and SD 4?

The groups are different.

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

1 z for 65

Subtract first: 65 minus 60 is 5.

Then 5 divided by 10 is 0.5.

2 z for 58

58 minus 50 is 8.

Then 8 divided by 4 is 2.

3 Compare

Careful!

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

Compare the z-scores.

2 is more than 0.5.

So 58 is better, compared with its own group.

4 Check

Let's check each z.

60 plus 0.5 times 10 is 65.

50 plus 2 times 4 is 58.

So both are right!

Let's look back.

First: z for 65.

Then: z for 58.

Then: compare.

Last: check.