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Math Help - How many beads in a jar?

  1. #1
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    How many beads in a jar?

    So I have been assigned a task of calculating the number of each color of beads in a jar that I am not allowed to open. The jar contains approximately 5000 beads as a rough estimate, and is filled to the top so shaking the jar will not shift any beads. There are about 20 different colors of beads inside the jar and the basic goal of the assignment is to be able to calculate with high accuracy the proportion of each color bead only by looking at the outside of the jar. Since the jar is square with rounded edges and is about twice as long as it is wide, my game plan is to break down each side of the jar into 2 halves, count all the beads on the outer layer recording colors, and calculate the proportions from each color of the 8 samples I will take (2 per side, 4 sides) and then average those proportions to remove some bias. Any other ideas on how you might sample the jar or comments on why my method may not work aside from the possibility of a clump of same colored beads in the center of the jar? (In case you were wondering this problem has been solved in the past in my class so there is a way to reliably sample and calculate the proportions)
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  2. #2
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    Re: How many beads in a jar?

    I think you're making it harder than it is. Since you don't give us the dimensions of the jar or marbles we'll just have to accept your value of 5000 for the number of marbles.

    Sample the entire outer layer of marbles. You will then have K marbles sampled resulting in C different colors and the number of marbles for each color being nc.

    Your estimate for the number of marbles of each color in the jar is then going to be

    $$\frac{5000}{K}n_c \mbox{ for }c=1, C$$

    you simply don't have any information that indicates you can do better with some other strategy.

    What you don't want to do however is process the data in pieces and then process the pieces. You want to process the raw data in one chunk.
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  3. #3
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    Re: How many beads in a jar?

    Thanks for the response! The actual number of beads in the jar is irrelevant for the calculation i need, I may have mislead you in my first sentence above. All i really need is the proportion of each color. The reason I didn't want to simply count all the beads visible and do a proportion from there is because that may not be truly representative of the dispersal of beads on the interior. By doing multiple samples of the same size and averaging proportions it should give a truer value so long as the same sizes are large enough, though I will likely try multiple methods and compare values
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