difference between standard deviation and mean absolute deviation

2 ANSWERS

1. jane
   

   hello
   
        The ‘standard deviation’ is a measure of 'dispersion' or 'spread'. It is used as a common summary of the range of scores associated with a measure of central tendency – the mean-average. It is obtained by summing the squared values of the deviation of each observation from the mean, dividing by the total number of observations1, and then taking the positive square root of the result2. For example, given the separate measurements:
   
   13, 6, 12, 10, 11, 9, 10, 8, 12, 9
   
   Their sum is 100, and their mean is therefore 10. Their deviations from the mean are:
   
   3, -4, 2, 0, 1, -1, 0, -2, 2, -1
   
   To obtain the standard deviation we first square these deviations to eliminate the negative values, leading to:
   
   9, 16, 4, 0, 1, 1, 0, 4, 4, 1.
   
   The sum of these squared deviations is 40, and the average of these (dividing by the number of measurements) is 4. This is defined as the ‘variance’ of the original numbers, and the ‘standard deviation’ is its positive square root, or 2. Taking the square root returns us to a value of the same order of magnitude as our original readings. So a traditional analysis would show that these ten numbers have a mean of 10 and a standard deviation of 2. The latter gives us an indication of how dispersed the original figures are, and so how representative the mean is. The main reason that the standard deviation (SD) was created like this was because the squaring eliminates all negative deviations, making the result easier to work with algebraically.
   
   THE MEAN DEVIATION
   
   There are several alternatives to the standard deviation (SD) as a summary of dispersion. These include the range, the quartiles, and the inter-quartile range. The most direct alternative for SD as a measure of dispersion, however, is the absolute mean deviation (MD). This is simply the average of the absolute differences between each score and the overall mean. Given the separate measurements:
   
   13, 6, 12, 10, 11, 9, 10, 8, 12, 9
   
   Their sum is 100, and their mean is therefore 10. Their deviations from the mean are:
   
   3, -4, 2, 0, 1, -1, 0, -2, 2, -1
   
   To obtain the mean deviation we first ignore the minus signs in these deviations to eliminate the negative values, leading to:
   
   3, 4, 2, 0, 1, 1, 0, 2, 2, 1.
   
   These figures now represent the distance between each observation and the mean, regardless of the direction of the difference. Their sum is 16, and the average of these (dividing by the number of measurements) is 1.6. This is the mean deviation, and it is easier for new researchers to understand than SD, being simply the average of the deviations – the amount by which, on average, any figure differs from the overall mean3. It has a clear meaning, which the standard deviation of 2 does not4. Why, then, is the standard deviation in common use and the mean deviation largely ignored?
   
   
   hope it helps

   Report (2) (1)  |   12 years, 8 month(s) ago  

2. Guest8150
   

   Wow, thanks. This is a fantastic answer. Just what i was looking for. Thanks again.

   Report (0) (0)  |   12 years, 8 month(s) ago