(57) Z scores - Statistics

A Z score indicates how many standard deviations an element is from the mean. It is calculated using the formula:

Z = (X - μ) / σ

Where:

• X is the value in question

• μ is the mean of the dataset

• σ is the standard deviation of the dataset. The Z score is calculated using the formula: Z = (X - μ) / σ, which indicates how many standard deviations a value is from the mean. A Z score can be positive or negative, reflecting whether the value is above or below the mean, respectively. A Z score of 0 indicates that the value is exactly at the mean, while Z scores greater than 0 signify values above the mean and Z scores less than 0 indicate values below the mean. In practical applications, Z scores are commonly used in standardizing scores from different distributions, allowing for comparison across diverse datasets. Z scores also play a critical role in identifying outliers, as values with Z scores greater than +3 or less than -3 are often considered statistically significant deviations from the mean.