Z-Score Calculator
Standard Score & Percentile โก
Calculate the z-score of any value given a mean and standard deviation, and find the corresponding probability and percentile.
Calculate the z-score of any value given a mean and standard deviation, and find the corresponding probability and percentile.
z = (X โ ฮผ) รท ฯ
Where X is the raw value, ฮผ (mu) is the population mean, and ฯ (sigma) is the standard deviation. A z-score tells you how many standard deviations a value is above or below the mean.
What is a good z-score?
It depends on the context. In academic testing, a z-score above 1.0 (top 84%) is generally considered above average. In quality control, values with |z| > 3 are often flagged as defects.
What is the difference between z-score and percentile?
A z-score measures distance from the mean in standard deviation units. A percentile tells you what percentage of the population scored below that value. They are related โ a z-score of 0 corresponds to the 50th percentile.
What is the normal distribution?
The normal distribution is a bell-shaped probability distribution where most values cluster around the mean. Z-scores assume data follows this distribution. About 68% of values fall within 1 standard deviation, 95% within 2, and 99.7% within 3.