How to find z score for percentile

To find z score for percentile, we check the percentile value in the center part of the normal distribution table. For example, find the z score of the 45th percentile.

z score of 45th percentile

The Z score for the 45th percentile is -0.13

Example two, find the z score of the 33rd percentile.

z score of 33rd percentile

The Z score for the 33rd percentile is -0.44

Percentile to z score formula

The formula of percentile to z score formula assumes that the underlying distribution is normal. The formula to calculate percentile to z score is given by;

Percentile to Z score formula deriving

Where T is the percentile

Notably, we can find the value of the z score of a percentile in excel using the excel function =Norm.Inv (T,0,1)

Where T is the percentile

0 is the standard mean

1 is the standard deviation

For example, consider the 40th Percentile, and find the z score in excel.

40th percentile z-score excel

Thus, the value will be;

z score of 40th percentile in excel

The Z-score for the 40th percentile is -0.25335

Examples to find z score for percentile

What z score represents the 95th percentile

The z-score that represents the 95th Percentile is 1.645

What z score represents the 90th percentile

The z-score that represents the 90th Percentile is 1.282

What z score represents the 80th percentile

The z-score that represents the 80th Percentile is 0.842

What z score represents the 75th percentile

The z-score that represents the 75th Percentile is 0.674

What z score represents the 85th percentile

The z-score that represents the 85th Percentile is 1.036

What z score represents the 20th percentile/2nd decile

The z-score that represents the 20th Percentile is -0.842

Z score percentile table/chart

Percentile Z-Score Percentile Z score
1 -2.326 51 0.025
2 -2.054 52 0.05
3 -1.881 53 0.075
4 -1.751 54 0.1
5 -1.645 55 0.126
6 -1.555 56 0.151
7 -1.476 57 0.176
8 -1.405 58 0.202
9 -1.341 59 0.228
10 -1.282 60 0.253
11 -1.227 61 0.279
12 -1.175 62 0.305
13 -1.126 63 0.332
14 -1.08 64 0.358
15 -1.036 65 0.385
16 -0.994 66 0.412
17 -0.954 67 0.44
18 -0.915 68 0.468
19 -0.878 69 0.496
20 -0.842 70 0.524
21 -0.806 71 0.553
22 -0.772 72 0.583
23 -0.739 73 0.613
24 -0.706 74 0.643
25 -0.674 75 0.674
26 -0.643 76 0.706
27 -0.613 77 0.739
28 -0.583 78 0.772
29 -0.553 79 0.806
30 -0.524 80 0.842
31 -0.496 81 0.878
32 -0.468 82 0.915
33 -0.44 83 0.954
34 -0.412 84 0.994
35 -0.385 85 1.036
36 -0.358 86 1.08
37 -0.332 87 1.126
38 -0.305 88 1.175
39 -0.279 89 1.227
40 -0.253 90 1.282
41 -0.228 91 1.341
42 -0.202 92 1.405
43 -0.176 93 1.476
44 -0.151 94 1.555
45 -0.126 95 1.645
46 -0.1 96 1.751
47 -0.075 97 1.881
48 -0.05 98 2.054
49 -0.025 99 2.326
50 0

 

What is a percentage rank?

Percentile rank (PR) of a given score in statistics refers to the proportion of scores lower than a given score in a frequency distribution.

To make the meaning of test results more understandable, percentile ranks are frequently used.

According to the test theory, the percentile rank of a raw score is understood to be the proportion of test-takers in the norm group who received a score lower than the score of interest.

Statistics professionals frequently use percentile rank to determine how an individual assessment score or outcome relates to others in a set.

Additionally, knowing the percentile rank can help one gain perspective on how well they did on a particular test.

ABOUT US

Edutized is a learning platform that offers tutorials in over 100  subject fields. We also offer free calculators in Statistics, Calculus, Math etc.

If you are looking for more assistance, post a question for our tutors to help your out directly or create a tutorial for you.

We create tutorials for all queries with a huge interest and post them for free on our website. 

Happy Learning!

Related Content