In what way does a z-score give an indication of how unusual a value is? the larger it is the more unusual it is.

The z-score is defined as the number of standard deviations that separate a certain observed value from the population mean. 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 or raw 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).