Z-Score Calculator

A Z-score (also known as a standard score) is a measurement of how many standard deviations a particular data point is from the mean of a set of data. It allows for the comparison of scores from different normal distributions, which is particularly useful in statistics and research.

The Z-score is calculated using the formula: Z = (X – μ) / σ, where X is the value being measured, μ is the mean of the population, and σ is the standard deviation of the population.

Z-scores can be positive or negative. A positive Z-score indicates that the data point is above the mean, while a negative Z-score indicates that the data point is below the mean. A Z-score of 0 means that the data point is equal to the mean.

In a standard normal distribution (mean = 0, standard deviation = 1), approximately 68% of values fall within one standard deviation of the mean (Z-scores between -1 and 1), about 95% fall within two standard deviations (Z-scores between -2 and 2), and about 99.7% fall within three standard deviations (Z-scores between -3 and 3).