Z Score and Percentile

A Z Score is a statistical measurement that describes a value's relationship to the mean of a group of values, expressed in terms of standard deviations from the mean.

Z Score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

A Z Score of -2 indicates that the value is 2 standard deviations below the mean.

The mean is 83.58.

It means that 55% of the class scored the same or worse than the student.

A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls.

Percentile Rank = (Number of values below X / Total number of values) * 100.

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

A Z Score of 0 indicates that the value is exactly at the mean.

The Z Score is -2.