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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.
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.
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.
What would it mean if a standard deviation was calculated to equal 0?
A standard deviation of zero means that all the data points are the same value.
What happens to the standard score as the standard deviation increases?
The absolute value of the standard score becomes smaller.
