Statistics
Z-Score Calculator
Standardise any data point against its distribution. Calculate the z-score, percentile rank, and probability for any value given the population mean and standard deviation.
Dataset Input
Valid formats: 12, 15.5, 20 or newline separated lists. Non-numeric values are automatically excluded.
Summary Metrics
Sample Size (n)10
Min / Max Range[12, 30]
Summation (Σx)212
Arithmetic Mean
21.2
Median Value
21.5
Modal Value
22
Std. Deviation
5.2688
Population Variance
27.76
Total Range Spread
18
Frequency Distribution
Dataset visualization across unique values
Share & Embed
Share your exact result or embed this tool.
Solution Methodology
01
Enter Value, Mean & SD
Provide the observed value x, population mean μ, and standard deviation σ.
02
Compute Z-Score
Apply z = (x − μ) / σ to standardise the observation.
03
Map to Probability
Use the standard normal CDF to find the one-tail p-value and percentile rank.
Common Questions
What does a z-score of 2 mean?
A z-score of 2 means the data point is exactly 2 standard deviations above the mean. In a standard normal distribution, approximately 97.7% of values fall below this point, placing it in roughly the 97.7th percentile.
How is z-score used to find probability?
After computing z = (x−μ)/σ, you look up (or compute) the cumulative distribution function Φ(z) of the standard normal distribution. Φ(z) gives the probability that a randomly selected value from the distribution is less than or equal to x.