Estatística Z (Z-Score) — Calculadora Online Grátis
Standardize data points with Z-score, percentile rank and normal distribution
The Z-Score Calculator converts any raw data value into a standardized score that shows how many standard deviations it lies from the mean. It also returns the corresponding percentile rank under the standard normal distribution. Statisticians, psychologists, educators, and quality control engineers use z-scores to compare values from different datasets on a common scale.
Frequently Asked Questions
Sobre Esta Calculadora
A z-score (also called a standard score) measures how many standard deviations a data point is from the mean of its distribution. A z-score of 0 means exactly at the mean, +1 means one standard deviation above, and −1.5 means 1.5 standard deviations below. The formula Z = (X − μ) / σ converts any value from any normal distribution to the standard normal distribution (mean=0, SD=1).
Z-scores are essential for comparing values from different distributions — for instance, comparing a student's performance on two exams with different means and standard deviations. They also enable calculation of percentile ranks by looking up the cumulative probability in the standard normal table.
Applications include standardized testing score reporting, Six Sigma quality control (a ±3σ process has only 0.27% defects), clinical reference ranges in medicine, IQ testing, and finance (z-scores form the basis of the Altman Z-score for predicting corporate bankruptcy).
Gere a probabilidade ou ranking numérico do aluno nos exames normatizados da distribuição perfeita e sem complicações acadêmicas complexas de mesa!
Fórmula
Z = (X - μ) / σ
Exemplo Resolvido
Z-score for a student who scored 88 on an exam with class mean 76 and SD 10
Entradas:
- Value (X): 88
- Mean (μ): 76
- Standard deviation (σ): 10
Passo a Passo:
- Formula: Z = (X − μ) / σ
- Z = (88 − 76) / 10 = 12 / 10 = 1.2
- A Z-score of 1.2 means the score is 1.2 standard deviations above the mean
- From the standard normal table: P(Z < 1.2) ≈ 0.8849
- Percentile rank ≈ 88.5th percentile