Units of measure do follow the standard deviation.
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Because it is in same units as the original data. For example, if you have a sample of lengths, all in centimetres, the sample variance will be in units of centrimetres2 which might be more difficult to interpret but the sample standard deviation with be in units of centimetres, which would be relatively easy to intepret with reference to the data.
Suppose the mean of a sample is 1.72 metres, and the standard deviation of the sample is 3.44 metres. (Notice that the sample mean and the standard deviation will always have the same units.) Then the coefficient of variation will be 1.72 metres / 3.44 metres = 0.5. The units in the mean and standard deviation 'cancel out'-always.
Yes, a standard deviation of 4.34 can be correct. Standard deviation is a measure of dispersion or variability in a data set. It represents the average amount by which individual data points deviate from the mean. Therefore, a standard deviation of 4.34 simply indicates that there is some variability in the data, with data points on average deviating by 4.34 units from the mean.
It depends on what you are trying to measure. There are different standard units for different characteristics.
The are effective as far as the domain of the random variable, and that domain may be infinite.