Difference between Standard Deviation and Variance.
In: Mathematics
In a nutshell, variance is the average of all differences from the mean . If you have a large sample that’s very well dispersed around the mean, the variance can be big. Taking a square root of the variance basically standardizes the differences – and tells you how the whole group varies from the mean.
I think the easy way to think about this is length of snakes (my teacher used snakes because no one in the class had any idea how long an average snake is); their length is 160, 180, 300, 54 and 120 cm. Which of these snakes is “long”? The mean is 162.8. That’s not that far from 160, so does that mean 180 is a particularly long snake? Variance is 6559.4 – it just means there’s a lot of differences in the snakes’ lengths. Standard deviation is sqrt(6559.4)=80.9. So, assuming that all snakes are represented by the population above, all snakes between 81cm and 243cm (160.8+/- 80.9) are within the range of “standard” lengths, and there’s only one really long and one really short snake in your sample.
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