# Will calculating standard deviations from percentages give different results to claculating them from the raw data?

I'll start off by saying I am not a mathematician, nor have I studied maths for many years, so please keep the answers simple :)

I am working with data that has a geographical context. So assume I have data about an area 10km by 10km. My data is split into 1km by 1mk tiles, so I have 100 rows of data. 1 row for each km square in my area.

Values in my data include the following, to name a few:

Number of buildings

Number of postcodes

% ground area covered by buildings in the km square

I am creating some cloropleth maps to give an overview of the whole area. I am symbolising the data using standard deviation so I can show which km squares are above and below the mean.

This works well for things such as building counts, so I know if a single km square is above or below the mean for the whole 100km area.

My question is, am I able to calculate the standard deviation for my % values? i.e. % ground area covered by buildings, % ground area covered by roads etc... Will this give me a sensible result?

Or would it be best to calculate the standard deviation on the actual area covered by these features in each km tile?

For the purpose of this answer I'll use the "% ground area covered by buildings". Since each of your data points corresponds to $1$ km by $1$ km tiles it actually doesn't "matter" if you use percentage or the raw data.
Say one tile contains $.25 \text{km}^2$ of buildings. Then the percentage covering is $25\%$. In general if the raw data is $X$ then the percentage is just is $100X$. In effect all this does is scale the standard deviation. You will find that if the standard deviation of the raw data (in those units) is $\sigma$, then the standard deviation of the percentage is $100\sigma$. Then how you symbolize these deviations can just take into account the difference in scaling.