Standard Score Calculator

The observation you want expressed in standard deviations.
Used by the "within a data set" mode to work out the mean and standard deviation first.
A z score of a member of the data set is conventionally taken against the population standard deviation.
One-sample z test only.
One-sample z test only.
z score
1.250000
Z-Score (Standard Score) Calculator
Raw score
85.000000
Percentile (area to the left)
89.4350 %
P(Z < z)
0.89435023
P(Z > z)
0.10564977
Two-tailed p-value
0.21129955
Mean used
70.000000
Standard deviation used
12.000000
T score (mean 50, sd 10)
62.500
Deviation score (mean 100, sd 15)
118.750
In words
1.25 standard deviations above the mean.
Worked out from NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.6.6.1 Normal Distribution and 2 other sources.
The z score itself assumes nothing about the shape of the distribution. The percentile and tail areas do: they are only percentiles if the underlying distribution is normal.

How this is worked out

2 steps
  1. z = (x - mu) / sigma = (85 - 70) / 12 = 1.25.
  2. Area to the left of z under the standard normal curve: Phi(1.25) = 0.89435023, i.e. the 89.435th percentile.

Results are general information, not financial, tax, legal, medical or engineering advice.