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In statistics, if we want to standardize the variables, we calculate the mean and standard deviation for a particular variable. Then, for each observed value of the variable, we subtract the mean and divide by the standard deviation.
Subtract mean and divide by standard deviation: Center the data and change the units to standard deviations. Subtract mean: Center the data. Divide by standard deviation: Standardize the scale for each variable that you specify, so that you can compare them on a similar scale.
Subtract the mean, , from the value you want to convert, X. Divide the result from Step 1 by the standard deviation, .
Subtract mean and divide by standard deviation: Center the data and change the units to standard deviations. Subtract mean: Center the data. Divide by standard deviation: Standardize the scale for each variable that you specify, so that you can compare them on a similar scale.
We subtract off the mean of X, which is , and divide through by the standard deviation of X, which is n, to obtain a standardised version of the sample mean: X/n.
When you standardize a random variable, its mean becomes zero and its standard deviation becomes one. therefore, if the Z score of x is zero, then the value of x is equal to the mean. if the Z score of x is one, then the value of x is one standard deviation above the mean.
The traditional way of standardizing variables is to subtract their mean, and divide by their standard deviation. Variables standardized this way are sometimes refered to as z-scores, and always have a mean of zero and variance of one.
The reason this importance is particularly high in cluster analysis is because groups are defined based on the distance between points in mathematical space. Standardization helps to make the relative weight of each variable equal by converting each variable to a unitless measure or relative distance.
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