Z-Score Calculator
Calculate standard scores and probabilities for normal distributions
Z-Score Results
Probability Information
Understanding Z-Scores: The Standard Score in Statistics
Our Z-Score Calculator helps you understand how a particular data point relates to a normal distribution. Z-scores are fundamental in statistics for comparing different data points across varying scales and distributions.
Did you know? A Z-score of 1.96 corresponds to the 97.5th percentile, which is commonly used in 95% confidence intervals in statistical testing.
What is a Z-Score?
A Z-score (or standard score) measures how many standard deviations a data point is from the mean of a distribution. The formula for calculating a Z-score is:
Z = (X – μ) / σ
Where:
- X is the data point
- μ is the population mean
- σ is the standard deviation
Interpreting Z-Scores
- Z = 0: The data point is exactly at the mean
- Z = 1: The data point is 1 standard deviation above the mean
- Z = -1: The data point is 1 standard deviation below the mean
- |Z| > 3: The data point is very unusual (in the tails of the distribution)
Practical Applications of Z-Scores
Z-scores are used across many fields:
- Education: Comparing test scores across different tests or populations
- Finance: Assessing how unusual a stock’s performance is relative to its history
- Healthcare: Evaluating whether a patient’s measurement is within normal ranges
- Quality Control: Identifying when a process is producing unusual results
- Psychology: Comparing individuals’ scores on standardized tests
Understanding Probability and Percentiles
Our calculator also shows the percentile rank and probabilities associated with your Z-score:
- Percentile Rank: The percentage of values in the distribution that fall below your data point
- Probability Below: The chance that a randomly selected value would be less than your data point
- Probability Above: The chance that a randomly selected value would be greater than your data point
Use our Z-Score Calculator to quickly analyze how your data point compares to a normal distribution. Remember that while Z-scores are powerful tools, they assume your data follows a normal distribution – results may be misleading for highly skewed data.