# How does standard deviation change with mathematical operations on the mean?

#### marinebioloj

##### New Member
Hi everyone,

while this question is not homework, I found it to basic to be put in the "research" category.
I am comparing nutrient uptake rates of algae under different conditions and have taken samples with three replicates after different times (but also from different beakers each time, so I guess they are independent?). To get the rate for a specific timeframe I have to substract the previous mean from each mean, then divide the result to get to the uptake per hour.

In short: Substract, divide, and sometimes also multiply means with standard deviations from and with each other or single numbers.

I am doing all of this in excel and so far my resulting SDs are not right, since I just tried to puzzle together formulas with the limited knowldge I have. There seems to be no concise guide for this online. Unfortunately, I do not understand a page long essay with a dozen sum signs and other operators, so I hope someone here can help me.

#### marinebioloj

##### New Member
Hi again,

is the question not good or thought too easy to solve?
For me it is not, unfortunately, but very important for my results.

#### JesperHP

##### TS Contributor
I am comparing nutrient uptake rates of algae under different conditions and have taken samples with three replicates after different times (but also from different beakers each time, so I guess they are independent?). To get the rate for a specific timeframe I have to substract the previous mean from each mean, then divide the result to get to the uptake per hour.
I do not fully understand youre calculations nor the statistical assumptions you are making from the above the description hence a general answer. One approach would be to use the delta method another would be to simulate and or bootstrap.

#### marinebioloj

##### New Member
Thank you for the quick reply!
I thought it might be important to know where the data came from, in case it made a difference in the formula I have to use. Maybe I wrote a bit confusing, so I added an excerpt from one of my data sets. The rest can be ignored for now. I do not know the methods you mentioned (or not those names at least) but I will look them up as well.