# Population vs sample variance

This is perhaps a very basic question, but I am a bit confused. I have a time series of day some time varying data, say the amount of sunlight as the day passes.

I bucket the data in say 10 bins say according to just time, so later bins occur later in time and calculate the variance of each of the bins. Is there a relationship between the calculated variances of the 10 bins and the overall population variance (variance of the whole data set)?

Suppose the i-th bin's variance is $V_i$, and the mean temperature in the i-th bin is $M_i$. Let $M$ be the mean temperature, and $\sigma$ the total variance. Then: $$\sigma = \sum\limits_{i=1}^{n} V_i + \sum\limits_{i=1}^{n}M_i (M-M_i)^2$$