# Population or Sample Standard Deviation: monthly climate data

I have daily mean temperature values for every day of every month for 90 years.

I want to figure out:

• "SD$_m$": the standard deviation of daily temps across all days in a given month, for each month

• "SD$_{yr}$": The standard deviation of monthly means for a given year, for each year.

My question: Do I use sample [s] or population [$\sigma$] standard deviations for each of these above calculations?

$$s = \sqrt{\frac{\sum_{i = 1}^N(x_i - \mu)^2}{N - 1}}$$

$$\sigma = \sqrt{\frac{\sum_{i = 1}^N(x_i - \mu)^2}{N}}$$

My goal is to compare SD$_m$ to SD$_{yr}$ via regression to gauge their relationship for developing a climate metric. My confusion comes from the fact that both metrics are calculated from the same data, but both metrics would qualify "population" differently (i.e., SD$_m$'s "population" consists of all days in each given month while SD$_{yr}$'s population consists of all months within a given year). Or am I thinking about this incorrectly??