Z-score

What Z-score is

A Z-score, also known as a standard score, is a numerical measurement used in statistics to indicate how many standard deviations a particular data point is from the mean of a given data set. It is calculated by subtracting the mean of the data set from the individual data point, and then dividing the difference by the standard deviation of the data set.

Steps for calculating a Z-score:

  1. Calculate the mean of the data set.

  2. Subtract the mean from each data point in the set and record the difference.

  3. Calculate the standard deviation of the data set.

  4. Divide each difference (from step 2) by the standard deviation.

  5. The resulting numbers are your Z-scores.

Examples

  1. Z-scores can be used to compare a given data point to the overall distribution of a dataset, allowing for the determination of whether a data point is an outlier.

  2. Z-scores are often used to standardize data in order to make it easier to compare different datasets.

  3. Z-scores can be used to calculate the probability of a given data point falling within a certain range.

  4. Z-scores can be used to measure the relative standing of a given data point within a dataset.

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