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nothing is important on math
Standard measurements make it easier for everyone to know what that measurement means. The metric system, which is the standard system used by scientists, is specifically designed to be easy to use. The English system is much more complicated, mathematically.
A z-score gives the distance (specifically number of standard deviations) from the mean so when you compare z-scores, it gives a direct comparison of how far from the mean the values are.
It is the normalised Gaussian distribution. To speak of a 'standard z' distribution is somewhat redundant because a z-score is already standardised. A z-score follows a normal or Gaussian distribution with a mean of zero and a standard deviation of one. It's these specific parameters (this mean and standard deviation) that are considered 'standard'. Speaking of a z-score implies a standard normal distribution. This is important because the shape of the normal distribution remains the same no matter what the mean or standard deviation are. As a consequence, tables of probabilities and other kinds of data can be calculated for the standard normal and then used for other variations of the distribution.
It is one of several measures of the spread of data. It is easier to calculate than the standard deviation, which has important statistical properties.