What does a z-score of 1.5 mean?

A z-score of 1.5 means the value is 1.5 standard deviations above the mean. In a normal distribution, this corresponds to approximately the 93rd percentile, meaning the value is higher than about 93% of all values.

Can z-scores be negative?

Yes, negative z-scores indicate values below the mean. For example, z = -1.2 means the value is 1.2 standard deviations below the mean.

What's considered a high or low z-score?

Generally, z-scores between -2 and +2 are considered normal (about 95% of data). Z-scores beyond ±2 are unusual, and beyond ±3 are very rare (less than 0.3% of data in a normal distribution).

How do I use z-scores to compare different datasets?

Z-scores standardize data, allowing comparison across different scales. For example, you can compare a test score (z = 1.2) with a height measurement (z = 0.8) to see which is relatively higher in their respective distributions.

Z-Score Calculator – Standard Score Calculator

Calculate z-scores, find probabilities, and convert between raw scores and standard scores. Essential for statistics and normal distribution analysis.

Z-Score Calculator – Standard Score Calculator

Calculate z-scores, find probabilities, and convert between raw scores and standard scores. Essential for statistics and normal distribution analysis.

Calculate*

What you want to calculate

Raw Score (X)

The raw score value

Mean (μ)*

Population or sample mean

Standard Deviation (σ)*

Population or sample standard deviation

Z-Score

The z-score value (for reverse calculations)

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Understanding Z-Scores

A z-score (standard score) tells you how many standard deviations a value is from the mean. It standardizes different distributions, allowing comparison between different datasets.

Interpreting Z-Scores

Z-score interpretation:

z = 0: Value equals the mean
z = 1: Value is 1 standard deviation above the mean
z = -1: Value is 1 standard deviation below the mean
z > 2 or z < -2: Value is considered unusual (more than 2 SD from mean)
z > 3 or z < -3: Value is considered very unusual or an outlier

How to Use This Calculator

Follow these simple steps to get accurate results:

Enter your calculate
Enter your raw score (x)
Enter your mean (μ)
Enter your standard deviation (σ)
Enter your z-score
Click the "Calculate" button to see your results
Review the detailed breakdown and explanation

Why Use Our Z-Score Calculator – Standard Score Calculator?

100% free and no registration required
Instant, accurate calculations with professional formulas
Mobile-friendly design that works on any device
Privacy-focused - your data never leaves your browser
Educational content to help you understand the results

Frequently Asked Questions

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