Need help on lab based on Millikan's experiment using masses

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The discussion revolves around a lab assignment based on Millikan's experiment, where participants must categorize approximately 50 mass samples into 8 groups to determine the mass of individual items, the number of items per container, and the mass of the containers. The user has derived a relationship between the total mass, container mass, and item mass but faces challenges due to multiple unknowns in their equations. They calculated differences between consecutive masses to simplify the problem but are still unable to isolate the variables effectively. The main issue lies in the reliance on average masses, which complicates finding exact values. The user seeks guidance on how to eliminate unknowns to progress in their calculations.
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Homework Statement


This lab is supposed to be an example of Millikan's experiment using masses. We were given a huge list of masses of different samples. Each sample contained a different amount of item. Each sample contained the same sample and the individual masses are the same. There were approximately 8 groups of samples. Each group contained different amounts of an item. Basically there were approximately 50 masses, and we had to divide the 50 into approximately 8 categories and find the average. The values that i got were:
m1 = 1284.625 (only contains 1 of the item)
m2 = 1523.89
m3 = 1796.625
m4 = 2033.56
m5 = 2301.22
m6 = 2549.18
m7 = 2797.125
m8 = 3061.67
m9 = 3269.125
I had to use these average masses to find the mass of each item, the number of items in each container, and the mass of the container.

Homework Equations


Q = ne - you don't actually use this equation directly.


The Attempt at a Solution


The first thing that i did was find an equation for the mass. I figured that the mass of the sample (m) must equal to the mass of the container (c) plus the number of items (n) times the mass of each item (I).
m = c + nI. n must be greater than equal to 1 and must be an integer.
For the first mass i got: 1284.625 = c + I (this is the relationship between the mass of the container and the item)
Either way, i have too many unknowns so i found the differences between the masses.
m2-m1 = 239.265
m3-m2 = 272.735
m4-m3 = 234.935
m5-m4 = 267.66
m6-m5 = 247.96
m7-m6 = 247.945
m8-m7 = 264.545
m9-m8 = 207.455
Since only the first one eliminates a variable i used that one.
239.625 = m2 - m1
239.625 = (c + nI) - (C + I)
239.625 = (n-1)(I) - this equation is for the increase in the number of items from one sample
i isolated for n and get n = (239.625 - I)/I.
I know that n has to be an integer, but the problem with this is that i used average masses. This could result in me not getting and exact value. Now at this point is where I am stuck. I have too many unknowns and can't really think of a way to eliminate one. Does anyone have any idea how to do this?
 
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does anyone know how to do this?
 
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