Z- Score

A statistical measure that quantifies the distance (measured in standard deviations) between a data point and the mean of the data set is said to be Z-Score . In other words ,
a Z-score or a standard score indicates how many standard deviations an observation or data is above or below the mean value.

It is a dimensionless quantity that is obtained by subtracting the population mean from the original  score and then dividing the difference by the population standard deviation.  The process of converting scores on a variable to Z-score is known as Standardization .

Why Z-Score ?
The Z-score is named so because ,  the normal distribution is also said to be "Z distribution". And they are often used to compare a data sample to a standard normal deviate though they can be defined without assumptions of normality.A Standard normal distribution,is the one where the mean value is 0 and σ value is 1),

Computation Of Z-Score :
The algorithm to compute a Z-Score is as mentioned below :

• Begin with a list of numbers representing the set of values of a data.
• Compute the mean of this list.(The mean is just a simple average )
• Then compute the standard deviation of the list of numbers. (The standard deviation is average distance between each number and the mean of the list)
• Now take a new number that you want to compare to the list of numbers. 
• Subtract the mean of that list from the number,
• Divide the result by standard deviation.
• The final result will be the Z-Score of new number compared to the list of numbers.

If the Z-Score is too low, we do not report an alert; rather we consider it to be noise. As Negative Z-score indicates that the original score is below the mean and Positive Z score means that the original score is above the mean value . A Z-Score says not only whether a point is above average or below average, but also how ‘unusual’ the measurement is .
Z-scores can also be called as Standard scores , z-values , normal scores, and standardized variables.

A vital point here is calculation of z requires population mean and population standard deviation, not the sample mean or sample deviation. Hence one needs to know the population parameters ,and not the statistics of a sample drawn from the population of interest
 
Applications :

The z-score is usually used in the z-test in standardized testing – the analog of Student's  t-test for  population whose parameters are known, instead of being estimated newly .As it is weird and unusual to know the entire population, one prefers using t-test .