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Statistics

Z-Score Calculator

A z-score measures how many standard deviations a value lies from the mean. This calculator applies z = (x − μ) / σ and explains whether the value is above or below the mean and by how much.

Z-Score Calculator

Standardize a value against a mean and standard deviation.

Try:
Answerz = 1.5
  1. Givenx = 85, μ = 70, σ = 10
  2. Formulaz = (x − μ) / σ
  3. Substitutez = (85 − 70) / 10 = 1.5
  4. Interpretation1.5 standard deviations above the mean
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Worked examples

z-score for x = 85, μ = 70, σ = 10 Standardize a single value to standard-deviation units. z-score for x = 72, μ = 80, σ = 4 A negative z-score puts the value two standard deviations below the mean.

Key terms

Mean The arithmetic average of a set of numbers — their sum divided by the count. Standard deviation A measure of how spread out the values in a data set are around the mean. Z-score The number of standard deviations a value lies above or below the mean. Normal distribution The bell-shaped probability distribution defined by a mean and a standard deviation.

Frequently asked questions

What does a z-score tell you?

It expresses a value's distance from the mean in standard-deviation units, allowing comparison across different data sets.

What is a negative z-score?

A negative z-score simply means the value is below the mean; a positive one means it is above.

What is considered an unusual z-score?

Values with |z| greater than about 2 are often treated as unusual, since they fall outside roughly 95% of a normal distribution.

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