Hence, we find out that our Z-Score is 1.33. Therefore, substituting the above values in our Z-Score formula, we get: Let’s say we pick a random student named Jacob with an height of 180cm ( x) and the mean ( μ) height for the students in the college is 160cm and the standard deviation ( σ) is 15. Let us understand how the Z-Score is calculated with the help of an example. But each of the elements in any dataset has a specific standard deviation. Z Score FormulaĪ dataset only has one mean value. Z score is a fundamental statistical calculation that is used for determining the relationship between the specified data and its dataset values.

Z-Score not only helps us determine both, Erica’s score in relation to other students as well as the exact position of her score in the data set. The answers to Erica’s question depends on other students’ score and Erica’s score in relation to them. These questions can be answered by organizing, analyzing, and interpreting the data set. This is where the Z-statistics and Z-Score come to play. She is curious what the average marks is for the class room. She is curious what percentage of the students have scored lower than her and what percentage of students have scored more than her. She is curious if majority of the students have scored higher or lower than her. Erica scores 62 marks out of 100 and is curious if she has scored better than the average. For example, let’s say the test scores of the students in a class are published.

In simpler terms, the Z score is the value of the deviation of a single data from its group mean value represented in terms of standard deviationĪ set of data only makes sense if any relevant information could be extracted from it. It is represented in terms of standard deviation. Z score of a value defines how far or close the position of a raw value is from the mean value of the set of data. It is a raw value’s relationship to a set of values. Z score is the position of a single data with respect to its mean value which is defined in terms of standard deviation.

More technically it’s a measure of how many standard deviations below or above the population mean a raw score is. Simply put, a z-score (also called as standard score) gives you an idea of how far from the mean a data point is.

Standard normal table for z scores