# Z-Score Calculator

A Z-Score Calculator is a statistical tool used to standardize data points and determine how many standard deviations a data point is away from the mean of a distribution. This calculation is important for understanding the relative position of a data point within a dataset and for making comparisons across different datasets. The formula used to calculate the Z-score involves the data point, the mean, and the standard deviation of the dataset.

The formula for calculating the Z-Score (Z) using the data point (X), the mean (μ), and the standard deviation (σ) is:

Z-Score (Z) = (X – μ) / σ

Where:

• Z-Score (Z) is the standardized score that represents the number of standard deviations a data point is away from the mean.
• Data Point (X) is the value of the individual data point.
• Mean (μ) is the average or arithmetic mean of the dataset.
• Standard Deviation (σ) is a measure of the dispersion or spread of the data points around the mean.

Using the Z-Score Calculator involves these steps:

1. Input: Enter the data point, the mean, and the standard deviation into the calculator.
2. Calculation: The calculator applies the formula to calculate the Z-score.
3. Output: The calculator displays the calculated Z-score.

This tool is particularly useful for statisticians, researchers, and analysts who need to assess the relative position of data points within a distribution and compare them to a standard or reference distribution.

For example, if you have a data point of 75, a mean of 60, and a standard deviation of 10, the Z-Score Calculator will provide you with the calculated Z-score, indicating how many standard deviations above the mean the data point is.

In statistics and data analysis, calculating Z-scores is essential for identifying outliers, assessing the significance of data points, and performing hypothesis testing.