Z-score Calculator

In statistics, a standard score is a multiple of a standard deviation, the value of which indicates how high or lower a raw score (the observed value or a point of the data) is above the average observed or measured value. Raw scores above average have a positive standard score and scores below average have a negative standard score.

The standard score is calculated by subtracting the average population from an individual raw score and then dividing it by the standard deviation of the population. This process of converting a raw score to a standard score is called normalization (although a standard score is not the only way to normalize).

Standard scores are usually called z-scores. These two words may be used interchangeably. Other terms include z-values, normal scores, and standard variables.

Calculate the z-score

If the mean population and the standard deviation of the population are known, the raw score x is converted to a level.

Such that:

• μ is equal to the average population.
• σ is the standard deviation of the population.

The absolute value of z represents the distance between that raw score x and the mean population in the same unit of standard deviation. When the raw score is below average, z is negative and when it is higher, it is positive.