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I very well know that Standard Deviation is the measure of spread of the data. If the data has higher deviation from its means then it has higher standard deviation.

What if the data has same mean and range and just a couple of values changed e.g.

Set1 : 10, 20, 50, 80, 90

Set2 : 10, 30, 50, 70, 90

Both have same range and mean, how can I compare the spreadness of the data without using the formula ?

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  • $\begingroup$ In the second set, a couple of items moved in towards the middle, so standard deviation went down. For how much, need to calculate. $\endgroup$ Commented Jul 1, 2013 at 14:58

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Note that standard deviation measures "squared differences" from the mean. Let's write down the squared differences for your data sets

Set 1: $40^2, 30^2, 0^2, 30^2, 40^2$,

Set 2: $40^2, 20^2, 0^2, 20^2, 40^2$.

As the mean of the first data set is larger, it has the larger mean squared deviation.

Or, with out calculating: As the data in the first set in mean are more far from the mean, it has the larger standard deviation.

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You may want to consider measures of dispersion other than standard deviation. For example the difference between symmetric quantiles is also a measure of "spread". Any quantile will do, if the spread between all of the others is equal. This immediately shows your Set 1 to have more "spread" than Set 2 merely by inspection; no calculation needed.

I'm still pounding on the probability book for the actuary test...

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