A Z-score is a statistical measure used in statistics of a value’s relation to the mean of a set of values, stated in terms of standard deviations from the mean. Professor Edward Altman founded it. If a Z-score is 0, then this implies that the data set value is equal as the average score. A 1.0 Z-score would indicate a deviation from the average, which is one SD. Z-scores may be positive or negative, with a score well above the average and a score slightly below the average (Salkind, 2019). When measured in SD units, a z-score represents the variability of a raw score in respect to the deviations from the mean. The z-score becomes positive if the output is above mean, and negative if less than average.
Importance of Z-Scores
It is helpful in the standardization of the variables (raw scores) of a normal distribution by integrating them into standard-scores since it helps statisticians to quantify the likelihood of results happening inside a normal distribution. It also enables statisticians to create comparisons between two scores from various experiments that may have different criteria and standard deviations and equate them (Salkind, 2019). It also allows for performance evaluation by optimizing the estimates on multiple types of variables. Standard distribution is an SND with an average of 0 and an SD of 1.
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How to Calculate the Z-Score
The formula for determining a z-score is z = (x-μ)/ÿ, in which x is the raw value, μ is the mean of a sample, and π is the standard deviation of the populace.
Z =
If the sample mean is unspecified, and the sample standard deviation is not known, the standard score will be calculated using the average sample (x̄) and sample standard deviation(s) as sample values measure.
How One Can Interpret a Z-Score
The z-score value informs one how many SD are alienated from the average value. If a z-score is 0, then it is on the average value. A strong z-score indicates that the actual value is above the mean. For instance, if a z-score is +1, 1 standard deviation is higher than the norm (Emerson, 2017). A negative z-score suggests the real score is lower than the average score. For example, if the z-score is comparable to -2, then two standard deviations are below the mean.
References
Emerson, R. W. (2017). Distribution of Scores around the mean and the Purpose of z-scores. Journal of Visual Impairment & Blindness, 111(1), 90-92.
Salkind, N. J., & Frey, B. B. (2019). Statistics for people who (think they) hate statistics. Sage Publications, Incorporated.
