The standarized or z-score is defined as the number of standard deviations that separate a certain observed value from the population mean. Therefore, this means it is used to quantify how unusual (far from the mean) a value is. The larger the z-score, the further the observed value is from the mean, and the more unusual. Z-score will be positive if the value is located above the mean and negative if located below.
As the formula in the picture indicates, the z-score is computed from the observed value by substracting the mean and by dividing the number obtained by the standard deviation afterwards. The result is the z-score with a mean of 0 and standard deviation of 1, and it can be represented in the normal distribution (picture 2).
Using the method described above, Judy can assess whether her bone density takes usual or unusual values.
