Normally when we standardize the different data points to compare the different data on the same scale.

But does it also make sense to standardize data points even when the different data points are already on the same scale?

For example, suppose that I have a dataset {x, y, z}, where x, y, and z are in the identical unit. Does it make sense to standardize these three data (i.e. subtract the sample mean of {x, y, z} from each x, y, and z, and then divide the quantities by the sample standard deviation of {x, y, z})?

If there are cases where such standardization can be useful, what are the examples of those cases?

Thank you,

But does it also make sense to standardize data points even when the different data points are already on the same scale?

For example, suppose that I have a dataset {x, y, z}, where x, y, and z are in the identical unit. Does it make sense to standardize these three data (i.e. subtract the sample mean of {x, y, z} from each x, y, and z, and then divide the quantities by the sample standard deviation of {x, y, z})?

If there are cases where such standardization can be useful, what are the examples of those cases?

Thank you,

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