Editing Standard score (section)

=== Comparison of scores measured on different scales: ACT and SAT ===
[[File:Z score for Students A.png|thumb|224x224px|The ''z'' score for Student A was 1, meaning Student A was 1 standard deviation above the mean. Thus, Student A performed in the 84.13 percentile on the SAT. ]]
When scores are measured on different scales, they may be converted to z-scores to aid comparison. Dietz et al.<ref name="Diez2012">{{Citation
|last1= Diez
|first1= David
|last2= Barr
|first2= Christopher
|last3= Çetinkaya-Rundel
|first3= Mine
|title= OpenIntro Statistics
|edition=Second
|year=2012
|publisher= openintro.org
|url=https://www.openintro.org/stat/textbook.php?stat_book=os
}}
</ref> give the following example, comparing student scores on the (old) [[SAT]] and [[ACT (test)|ACT]] high school tests. The table shows the mean and standard deviation for total scores on the SAT and ACT. Suppose that student A scored 1800 on the SAT, and student B scored 24 on the ACT. Which student performed better relative to other test-takers?

{| class="wikitable"
|-
!
! SAT
! ACT
|-
! Mean
| 1500
| 21
|-
! Standard deviation
| 300
| 5
|}
[[File:Z score for Student B.png|thumb|The ''z'' score for Student B was 0.6, meaning Student B was 0.6 standard deviation above the mean. Thus, Student B performed in the 72.57 percentile on the SAT. ]]
The z-score for student A is <math>z = {x- \mu \over \sigma} = {1800- 1500 \over 300} = 1 </math>

The z-score for student B is <math>z = {x- \mu \over \sigma} = {24- 21 \over 5} = 0.6 </math>

Because student A has a higher z-score than student B, student A performed better compared to other test-takers than did student B.