![]() ![]() ![]() The z-score can be used to normalise a set of values in a normal distribution by calculating the z-score of every value in the data set. The Probability Density Function of the Z-Distribution Calculate the probability of a particular score occurring.Compare scores that have different means and standard deviations.It is a value that describes how many standard deviations a result is from its mean.Ĭalculating the z-score is useful because it allows us to: The z-score is calculated using the following formula:Ī z-score does not have any units. This is because an outlier can be defined as a value that is more than 3 standard deviations above or below the mean.Ĭalculating the z-score is used to compare scores from different sets of data that have different means and standard deviations. Z-scores greater than +3 or less than -3 are considered outliers. Z-scores close to zero indicate that the result is close to the mean, whereas larger or very negative z-scores indicate that the result is further from the mean. Negative z-scores indicate raw scores that are below the mean and positive z-scores indicate raw scores which are above the mean. In other words, the raw score is zero standard deviations away from the mean and is therefore equal to the mean. ![]() This can be seen in the diagram below in which the position of the z-scores are labelled on the horizontal axis.Ī z-score of zero means that the raw score is identical to the mean. For example, a z-score of 2 means two standard deviations above the mean and a z-score of -1 means one standard deviation below the mean. Negative z-scores indicate a position below the mean. The z-score describes how many standard deviations a raw score is above the mean. ![]()
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