Definition of Z-Score

Z-Score is also known as standard score shows how standard deviated is an element from the mean. This can be calculated using the following formula:

z = (X – μ) / σ

Here, z = z-score, X = the value of the element, μ = population mean, and σ = standard deviation.

Explanation

• If it is less than 0, it represents an element less than the mean.
• If it is greater than 0, it represents an element greater than the mean.
• If it is equal to 0, it represents an element equal to the mean.
• It is equal to 1 means an element is 1 standard deviation greater than the mean; It is equal to 2 means an element is 2 standard deviations greater than the mean and so on.
• It is equal to -1 represents an element is 1 standard deviation less than the mean; it is equal to -2 means an element is 2 standard deviations less than the mean and so on.
• If the elements are in large number, then approximately 68% of the elements have z-score which lie between -1 and 1; around 95% of the elements have scored between -2 and 2; while, about 99% of the elements have Z-S which lie between -3 and 3.

Advantages

It enables us to understand the standard deviation of elements from the mean. In case of normally distributed data, 95% of the data lies between the z-score of -2 and 2. It also helps in comparing individual scores from different data sets. Additionally, through z-score scores of different sets of data can be standardized.