Step by step
The question
Question: find the z-score of 62, when the mean is 50 and the SD is 8.
z-score of 62: mean 50, SD 8
A z-score tells how many SDs a number is from the mean.
z = how many SDs from the mean
1 Write the formula
z is x minus the mean, all over the SD.
z = x − meanSD
Careful!
Subtract first, then divide.
The whole top is divided by the SD.
Careful: not 62 − 508 ✗
2 Put the numbers in
The top first: 62 minus 50 is 12.
Then 12 divided by 8 is 1.5.
z = 62 − 508 = 128 = 1.5
3 Read it
62 on a number line with the SD marks.
The z numbers count the SDs.
So 62 is 1.5 SDs above the mean.
1.5 SDs above the mean
4 Check
Let's check: start at the mean and go 1.5 SDs.
50 plus 1.5 times 8 is 62.
So it is right!
50 + 1.5 × 8 = 62
Let's look back.
First: write the formula.
Then: put the numbers in.
Then: read it.
Last: check.
Answer
z = 62 − 508 = 128 = 1.5