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Distinguish between mean deviation and standard deviation?
The mean deviation for any distribution is always 0 and so conveys no information whatsoever. The standard deviation is the square root of the variance. The variance of a set of values is the sum of the probability of each value multiplied by the square of its difference from the mean for the set. A simpler way to calculate the variance is Expected value of squares - Square of Expected value.
What is the difference between standard deviation and mean?
The mean is the average value and the standard deviation is the variation from the mean value.
How standard deviation and Mean deviation differ from each other?
There is 1) standard deviation, 2) mean deviation and 3) mean absolute deviation. The standard deviation is calculated most of the time. If our objective is to estimate the variance of the overall population from a representative random sample, then it has been shown theoretically that the standard deviation is the best estimate (most efficient). The mean deviation is calculated by first calculating the mean of the data and then calculating the deviation (value - mean) for each value. If we then sum these deviations, we calculate the mean deviation which will always be zero. So this statistic has little value. The individual deviations may however be of interest. See related link. To obtain the means absolute deviation (MAD), we sum the absolute value of the individual deviations. We will obtain a value that is similar to the standard deviation, a measure of dispersal of the data values. The MAD may be transformed to a standard deviation, if the distribution is known. The MAD has been shown to be less efficient in estimating the standard deviation, but a more robust estimator (not as influenced by erroneous data) as the standard deviation. See related link. Most of the time we use the standard deviation to provide the best estimate of the variance of the population.
How to calculate the standard deviation?
Suppose you have n observations {x1, x2, ... , xn} for a variable, X. Calculate m = (x1 + x2 + , ... , + xn)/n, the mean value. Calculate s2 = (x12 + x22 + , ... , + xn2)/n Then Variance = s2 - m2 = [mean of the squares] - [square of the mean] and the standard deviation = sqrt(Variance)
Sample standard deviation?
Standard deviation in statistics refers to how much deviation there is from the average or mean value. Sample deviation refers to the data that was collected from a smaller pool than the population.
