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What happens to the standard score as the standard deviation increases?
The absolute value of the standard score becomes smaller.
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.
Why the mean absolute deviation is calculated using absolute value?
The absolute value is used in the calculation of mean absolute deviation to eliminate negative differences. By taking the absolute value of each difference, it ensures that all values are positive, allowing for an accurate measure of the average deviation from the mean.
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.
What is an absolute deviation?
An absolute deviation is the difference between a given value and a variate value in statistics, or, in target shooting, the shortest distance between the centre of the target and the point where the projectile hit.
