# What effect does standardizing into z-scores have on the center (mean) of a variable?

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What effect does standardizing into z-scores have on the center (mean) of a variable?

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Step 1

What is Z-score and standardized variables:

Z-score:

The Z-score measures a particular value’s relationship to the mean in a group of values. It gives the number of standard deviation from the mean for the particular data point.

The general formula to obtain Z-score is,

Z = (x – population mean) / population standard deviation.

Standardized variables:

Standardized variables are the variables which are rescaled using the Z-score and these variables will have mean 0 and standard deviation 1.

Step 2

Find the effect of standardizing into z-scores on the centre of a variable:

From the definition of z-score and standardized variables, it is known that the mean of the standardized variable will be equal to “0”.

That is, standardizing into z-sc...

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