What is mean by Z Score?

joshi.murgha said:
Hey Friend's, i am looking for concept, Example and definition of Z Score. Can anyone like to help me?
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Hi Friend,

here are the Definitions of Z-Score

Define 1) In statistics, the standard score is the (signed) number of standard deviations an observation or datum is above the mean. Thus, a positive standard score represents a datum above the mean, while a negative standard score represents a datum below the mean. It is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing (however, "normalizing" can refer to many types of ratios; see normalization (statistics) for more).

Standard scores are also called z-values, z-scores, normal scores, and standardized variables; the use of "Z" is because the normal distribution is also known as the "Z distribution". They are most frequently used to compare a sample to a standard normal deviate (standard normal distribution, with µ = 0 and s = 1), though they can be defined without assumptions of normality.

The z-score is only defined if one knows the population parameters; if one only has a sample set, then the analogous computation with sample mean and sample standard deviation yields the Student's t-statistic.

The standard score is not the same as the z-factor used in the analysis of high-throughput screening data though the two are often conflated.

Define 2)

Z Score refers to the number of standard deviations the score( the data element) is away from the mean of the given distribution. It can be positive, negative or 0. It helps is better comparison of data with different groups of data through the process of standardization.

It is done as under:

Z-S core= (Score- Mean) /Standard Deviation

A Z score=0 means that the element is same as the mean. If it is positive then the element is above group mean and if it is negative then it is below group mean.

Example: Z score=1 means that the element is 1 standard deviation above the group mean
 
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