What does a z-score of 0 mean?

A z-score of 0 means the value equals the mean. Negative z-scores indicate values below the mean, positive z-scores indicate values above the mean.

What does a percentile tell me?

A percentile tells you what percentage of values in a normal distribution fall below your observed value. For example, a 84th percentile means 84% of values are below yours.

How do I use z-scores for hypothesis testing?

Compare the p-value to your significance level (typically 0.05). If p-value < 0.05, the result is statistically significant. Use one-tailed for directional tests, two-tailed for non-directional.

What is the 68-95-99.7 rule?

In a normal distribution: ~68% of values fall within 1 standard deviation, ~95% within 2 standard deviations, and ~99.7% within 3 standard deviations of the mean.

What is the difference between one-tailed and two-tailed p-values?

One-tailed p-values test if a value is extreme in one specific direction. Two-tailed p-values test if a value is extreme in either direction and are generally more conservative.

Z-Score Calculator

Free z-score calculator. Find the standardized score, percentile rank, one-tailed and two-tailed p-values for hypothesis testing and statistical analysis.

Calculate z-scores, percentiles, and p-values to standardize and interpret data relative to a normal distribution.

z = \frac{x - μ}{σ}

Related calculators

Standard Deviation Calculator

Calculate population and sample standard deviation, variance, and mean for your dataset.

Average Calculator

Calculate mean, median, mode, sum, and range for any list of numbers.

Descriptive Statistics Calculator

Get complete statistical summary: min, max, mean, median, mode, quartiles, variance, and standard deviation.

Percentage Calculator

Calculate percentages instantly: X% of Y, X is what % of Y, or percentage change.