I was not sure whether I should post this in Biology Stack Exchange or Math Stack Exchange so I posted it in both.
I was planning on doing a small research for my math class (a final project for the year) on population dynamics. I am going to use yeast cells and I will approximate the population of cells per medium (there will be several containers with yeast cells) using a colorimeter and a microscope. I will then graph the results to find a logarithmic regression for the graph that best represents the data, then I'd find the growth rate of the population of yeast cells. Up to here I have no issues.
I also wanted to calculate a distribution curve for the size of the yeast cells at three different points of the growing phase, t1, t2 & t3 (I would take a sample of the mediums with yeast cells, and using a microscope and a grid I would approximate the size of the yeast cells and separate them by size). The problem is that each sample will most likely have a different total number of cells (also varying depending on the medium). This would mean that the samples I take at, for example, t1 , will have a different total number of cells in them, thus making it impossible for me to average the number of cells with a size between two intervals. I do not want to average the total number of cells mainly because a sample might have 50 cells in it meanwhile another might have 200 cells in it.
Additionally, I wanted to make a binomial distribution too, by classifying the cells as either dead or alive (at t1, t2 & t3). I would calculate the probability of a cell being dead or alive by calculating the ratio between alive cells and total number of cells (I am not sure if this is also correct). Nonetheless, I face the same problem here: there will be different values regarding the total amount of cells per sample.
My question is: should I average the total number of cells per sample? Or is there some other way I can approach this problem?