Standard deviation has the same unit as the data set unit.
The answer depends on the individual measurement in question as well as the mean and standard deviation of the data set.
The formula for standard deviation has both a square (which is a power of 2) and a square-root (a power of 1/2). Both must be there to balance each other, to keep the standard deviation value's magnitude similar to (having the same units as) the sample numbers from which it's calculated. If either is removed from the formula, the resulting standard deviation value will have different units, reducing its usefulness as a meaningful statistic.
Standard units are used for measurmen as there is a system called the SI units and that is considered as the international system of units that is why we use standard units for measurment .
Information is not sufficient to find mean deviation and standard deviation.
Standard deviation is the square root of the variance.
The standard deviation has the same measurement units as the variable and is, therefore, more easily comprehended.
Units of measure do follow the standard deviation.
They are effectively the same but the standard deviation is more popular because the units of measurement are the same as those for the variable.
One can't associate a standard deviation with a single measurement like this.
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.
The answer depends on the individual measurement in question as well as the mean and standard deviation of the data set.
The "z-score" is derived by subtracting the population mean from the measurement and dividing by the population standard deviation. It measures how many standard deviations the measurement is above or below the mean. If the population mean and standard deviation are unknown the "t-distribution" can be used instead using the sample mean and sample deviation.
Standard Deviation
Units of measurement provide a standard to measure mass, length etc.So, it is useful.
units
Standard deviation is often considered the best measurement for dispersion because it quantifies the amount of variation or spread in a dataset relative to the mean. Unlike range or interquartile range, standard deviation takes into account all data points, allowing for a more comprehensive understanding of variability. It also has a direct mathematical relationship with other statistical measures, making it useful for further analysis, particularly in normally distributed data. Additionally, it is expressed in the same units as the data, facilitating easier interpretation.
The mean is 12 and each observation is 8 units away from 12.