Z-Score Calculator

Understand where your data point stands in a distribution. Calculate the Z-score and visualize it on the normal distribution curve.

Input Parameters

Enter the data point, mean, and standard deviation to calculate the Z-score.

Data point (x)

Mean (μ)

Standard deviation (σ)

Result

Z-score:

The Z-score represents the number of standard deviations your data point is away from the mean.

Formula: $$Z = rac{x - \mu}{\sigma}$$

Normal Distribution Visualization

What is a Z-Score?

A Z-score, or standard score, tells you how many standard deviations a particular data point is from the mean of its distribution. It's a way to standardize data, allowing for comparison across different datasets. A positive Z-score indicates the data point is above the mean, while a negative Z-score indicates it's below the mean. A Z-score of 0 means the data point is exactly at the mean.

Formula: $$Z = rac{x - \mu}{\sigma}$$ where $x$ is the data point, $\\mu$ is the mean, and $\\sigma$ is the standard deviation.
Use Cases: Identifying outliers, comparing data from different distributions, hypothesis testing in statistics.
Interpretation: Z-scores are typically interpreted in the context of the standard normal distribution. For instance, approximately 68% of data falls within a Z-score of ±1, 95% within ±2, and 99.7% within ±3.

Sources: Wikipedia, Investopedia