Calculadora de Z-score

The Z-score Calculator is a statistical tool that computes the standardized score of a value relative to a normal distribution. The z-score indicates how many standard deviations a data point is above or below the mean. The formula used is z = (x − μ) / σ, where x is the observed value, μ is the population mean, and σ is the standard deviation. This calculation is essential for comparing data from different distributions or identifying outliers.

How it works: you enter the value x, the mean, and the standard deviation. The calculator applies the formula and returns the z-score. This number can be used to find the cumulative probability in the standard normal table. For example, a z-score of 1.5 means the value is 1.5 standard deviations above the mean. The tool is useful for statistics students, researchers, and professionals who analyze normalized data.

When to use: in hypothesis testing, to standardize exam scores (like ENEM or SAT), in quality control to detect out-of-spec parts, or in finance to assess investment risk (Altman Z-score). It is also used in psychometrics to interpret IQ tests. The calculator simplifies the manual process and avoids calculation errors.

Cautions: the z-score assumes the data follows a normal distribution. If the distribution is highly skewed, the result may be misleading. Additionally, use population mean and standard deviation (not sample) for accuracy. Ensure the entered values are coherent: the mean should be within typical values and the standard deviation must be positive.