[Math] Compare standard deviation with out using the standard formula

standard deviation

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 ?

Best Answer

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.