What is a Z-score?

A Z-score is a quantitative metric that defines a value's association with the mean of a set of values. It shows in standard deviations from the mean.

Z-Score equation: z = (X - μ) / σ In this equation, X is a data point, μ signifies the mean, and σ indicates the standard deviation.

How to use the Z-score Calculator?

This Z-score calculator measures the distance of a data point from the mean. 1. Enter the data point (X) – X is the value you want to analyse. 2. Enter the mean (μ). 3. Enter the Standard deviation (σ).

After putting the values, you click the key on the calculator, and you will see the results in seconds.

Example:

Data point (X) = 25

Mean (μ) = 15

Standard deviation (σ) = 4

Step 1: Z-Score formula: z = (X - μ) / σ

Step 2: z = (25 - 15) / 4

Step 3: z = 10 / 4 = 2.5

Step 4: 2.5

How does the Z-score work?

The free MathCalc Z-score calculator uses the Z-score formula to measure the distance of a data point from the mean in standard deviation units. It subtracts the mean from the data point and divides the result by the standard deviation. It returns a positive or negative number showing the position relative to the mean.

Why use the MathCalc Z-score calculator?

Get Quick Results

Finding the Z-score by hand can take time, especially when dealing with large numbers. This free MathCalc calculator gives accurate results in seconds. Example: If you are finding the Z-score of X (60), μ (70), σ (4) by hand, it takes a long time and effort, but the MathCalc Z-score calculator gives an accurate result (-2.5) in seconds.

Reduce Human Error

Manual math can lead to minor mistakes that cost you money or points. This tool provides proven formulas to reduce errors, and your results are always right. Example: If you are finding the Z-score of X (80), μ (60), σ (4) by hand, it is easy to create mistakes, but the MathCalc Z-score calculator gives an accurate result (5) in seconds.

User-Friendly

This free MathCalc Z-score calculator has a simple interface. It works perfectly on every device. It is user-friendly and valuable for students and teachers.

Tips for Best Results:

Always use the correct mean and standard deviation for your dataset.

Always double-check your input.

Remember positive = above mean, negative = below mean.

FAQ

Can the Z-score be negative?

Yes! A negative Z-score means the value is below the mean.

What does a Z-score of 0 mean?

It means the value is exactly equal to the mean.

Do Z-scores work only for normally distributed data?

While Z-scores are most useful for normally distributed data, they can still be calculated for any dataset.