I'm a first year A level student studing maths, further maths, biology and chemistry. In maths, we find the standard deviation by dividing by n. In biolgy, we find the standard deviation by dividing by n-1. I'm not entirely sure why we use different formulas in the two subjects when they're at the same level, and it's causing quite a bit of confusion.
Thanks in advance if anyone can explain this to me.
If you have a sample - a set of $n$ observations or results or trials $\{x_i\}$- then the variance of the sample is
$s_n^2 = \frac 1 n \sum (x_i-\bar x_i)^2$
However, in biology and other sciences, usually we are more interested in the statistics of the whole population (from which the sample is drawn) rather than the sample itself. And it turns out that a better estimate of the variance of the whole population is
$s^2 = \frac 1 {n-1} \sum (x_i-\bar x_i)^2$
The correction from $n$ to $n-1$ is known as Bessel's correction.