Z-score Calculator
以下详细说明暂以英文提供。
What standardizing buys you
A z-score re-expresses a value in units of standard deviations away from the mean: z = (x − μ) ÷ σ. Scoring 85 when the class averaged 75 with a standard deviation of 10 puts you exactly one standard deviation high, z = 1 — a statement that no longer depends on the test’s scale. That shared scale makes comparisons across different measurements fair, and it plugs straight into the normal distribution: about 68% of values fall within z = ±1, 95% within ±2, and 99.7% within ±3. The percentile shown here integrates the normal curve up to your z, so z = 1 corresponds to roughly the 84th percentile.
常见问题
Can a z-score be negative?
Yes — a negative z simply means the value sits below the mean. z = −1.5 is one and a half standard deviations under average, and it still converts to a percentile via the normal curve.
Does the percentile always apply?
Only when the data is roughly bell-shaped. The z-score itself is always valid arithmetic, but the percentile row relies on normality; for strongly skewed data, use the median and quartiles instead.