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Why range is not considered as a good measure of variability? Why standard deviation is preferred over the other measures?”
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The standard deviation and range are both measures of the spread of a data set. Each number tells us in its own way how spaced out the data are, as they are both a measure of variation. The range relies on a very simple formula of subtracting the minimum data value from the maximum. The standard deviation is a more reliable measure of variation, and is less susceptible to outliers, however the calculation for the standard deviation is more involved than that of the range. Although there is a not an explicit relationship between the range and standard deviation, there is a rule of thumb that can be useful.
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Standard deviation makes use of all data to calculate the spread of data from average while range only uses two data ie the largest value data and the smallest value data, so standard deviation is a more accurate measure.
In addition, standard deviation measures the spread of data from the MEAN while range measures only the two extreme values ie the difference between the largest value and smallest value data.
Thirdly, standard deviation can be used in the statistical analysis eg hypothesis testing.
Fourthly, standard deviation gives weightage to the deviation of the data from the mean by squaring it ie the greater the deviation, the greating the weightage after the squaring.
Fifthly, standard deviation gives weightage to the positive and negative deviation of the data from the mean too.
Hence, Standard deviation is a more precise measure of spread of data as compared to the rudimentary range measure of the spread of data.
SD's has the following values due to which its best then others variables....
1) It is rigidly defined.
2) It is based on all the observations of the series and hence it is representative.
3) It is amenable to further algebraic treatment.
4) It is least affected by fluctuations of sampling.
there are three measure of variability range, inter quartile range and standard deviation. now what is that reason that standard deviation is more preferable among these three methods/
The range is the difference between the largest and smallest values in a set of values.
For example, consider the following numbers: 1, 3, 4, 5, 5, 6, 7, 11. For this set of numbers, the range would be 11 - 1 or 10.
Basically, because the range of a set of data is completely determined by just two of them -- the min and the max values. As long as all the other values stay between those two bounds, the range stays the same.
The std. dev. on the other hand, depends on every value in the dataset.
For example, if a set of 100 data consists of 10 and 50, with all the rest of them between 24 and 26, the range will be 40; the semi-range, 20. The std. dev. will be close to 1, however.
Then if another set of 100 consists of the same extremes: 10 and 50; but the rest of them are scattered evenly between those extremes, the semi-range is still 20; but now, the std. dev. will be a lttle more than 10.
Another example:
If you have two datasets, both normally distributed with the same std. dev., but one with 100 times as many data as the other, then the larger dataset will tend to have a much larger range than the smaller one; but both have the same variability.
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