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Free online Z-Score calculator to find standard scores, percentiles, and probabilities. Calculate how many standard deviations a value is from the mean instantly.
Calculate standard scores and percentiles
A Z-Score (also called a standard score) is a statistical measurement that describes a value's relationship to the mean of a group of values. It measures how many standard deviations below or above the population mean a raw score is.
The Z-Score formula is: Z = (X - μ) / σ
This calculator is developed by statistical experts and follows standard statistical formulas used in academic and professional settings. All calculations are verified for accuracy.
Enter the Value (X): Input the data point you want to analyze
Enter the Mean (μ): Input the average of your dataset
Enter Standard Deviation (σ): Input the standard deviation of your dataset
Click Calculate: Get instant results with Z-Score, percentile, and interpretation
About 68% of data falls within 1 standard deviation of the mean. These values are typical and expected.
About 27% of data falls in this range. These values are somewhat uncommon but not rare.
About 4.3% of data falls here. These values are statistically significant and warrant attention.
Less than 0.3% of data. These are outliers and very rare occurrences.
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A Z-Score (or standard score) measures how many standard deviations a data point is from the mean. It's calculated using the formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
Z-Scores are interpreted as follows: |Z| < 1 indicates the value is within 1 standard deviation (typical), |Z| between 1-2 is slightly unusual, |Z| between 2-3 is unusual/significant, and |Z| > 3 is very rare/extreme.
A 'good' Z-Score depends on context. In general, Z-Scores between -2 and +2 are considered normal (covering about 95% of data). Values beyond ±3 are considered outliers.
Yes, a negative Z-Score indicates that the value is below the mean, while a positive Z-Score indicates it's above the mean. The magnitude shows how far from the mean it is.
A Z-Score measures standard deviations from the mean, while a percentile indicates the percentage of data below a given value. They're related: a Z-Score of 0 corresponds to the 50th percentile.
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