![]() It basically measures how much a raw score value is standard deviation above or below the mean of the distribution. Z-score tells us how far the raw score value is from the mean of the distribution. In most cases, the Z score lies within 3 standard deviations below or above the mean of the distribution. ![]() If the Z-score is negative, it tells that the raw score value is below the mean of the distribution.If the Z-score is positive, it tells that the raw score value is above the mean of the distribution.it is zero standard deviation away from the mean. If the Z-score is zero, it tells that the raw score value is equal to the mean of the distribution, i.e.Z score value can be positive, negative, or zero. Z score calculated tells your score is 1.75 standard deviations above the mean as it has a positive value. Input values in the z score formula to calculate the value below The Mean of the test has 135 and a standard deviation of 20. Let’s understand z score calculation with an example as given below:įor example, let’s say you have scored 170 marks on the statistics test. This computational procedure is called standardizing raw scores. The Z-score is a dimensionless measure since it is derived by subtracting the population mean from an individual raw score and then this difference is divided by the population standard deviation. It allows us to calculate the probability of a score occurring within the same normal distribution.This is achieved by converting raw to standardized scores. ![]() It allows a comparison between two scores that are from different normal distributions.Z score is a very useful and important statistic because In such a case, the z score is calculated using the sample mean and sample standard deviation as below Z score value calculated using the z-score formula represents the distance of raw score x value in the units of standard deviation from the mean value.Ī Z-Score formula can also be represented as below when the mean of population and population of standard deviation is unknown. Σ = is the population standard deviation for the unstandardized value Μ = is the population mean for the unstandardized value If the population mean and population standard deviation are known, the Z score is calculated using the below formula Z-Scores – Standard Normal Distribution Using Z-Score Formula
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