Compare 80 (mean 70, sd 5) and 85 (mean 75, sd 10)

Step by step

The question

Question: which is better, 80 in a group with mean 70 and SD 5, or 85 in a group with mean 75 and SD 10?

The groups are different.

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

1 z for 80

Subtract first: 80 minus 70 is 10.

Then 10 divided by 5 is 2.

2 z for 85

85 minus 75 is 10.

Then 10 divided by 10 is 1.

3 Compare

Careful!

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

Compare the z-scores.

2 is more than 1.

So 80 is better, compared with its own group.

4 Check

Let's check each z.

70 plus 2 times 5 is 80.

75 plus 1 times 10 is 85.

So both are right!

Let's look back.

First: z for 80.

Then: z for 85.

Then: compare.

Last: check.