# Sampling to figure most common color in M&M packet

1. Jun 27, 2008

### musicgold

Hi,

I am struggling with a problem and do not know how I should approach it.

I went to a baseball game with my son, where I bought him a packet of M&Ms. While eating the candy, my son asked me what color most of the M&Ms are. At first, I intended to tell him that there are equal numbers of M&Ms of every color, but then I decided to do an experiment. I asked him to randomly take out 10 M&Ms from the packet, without replacing them back. We had the following sample.

Br Br Br Br Y Y R O O G

Where, Br= Brown, Y=Yellow, R=Red, O=Orange, G= Green, B= Blue.
Altogether, there were six colors and about 150 M&Ms in that 150-gm packet.

Seeing this, I was not sure what answer to put forward. I asked him to draw one more sample. The second sample was as given below.
O O O O O O O Y R B

Now I was totally confused. I realized that I need to brush up on my Probability and Stats knowledge. Here are the questions I am struggling with.

1. How can I find the most common color using the sampling approach?
2. What was wrong with my approach to the problem?
3. What would I need to do if I wanted to find the two most common colors in a packet?
4. How can I calculate the standard deviation of a sample in this kind of experiment?

Thanks,

MG.

2. Jun 27, 2008

### matt grime

There are many statistical tests you can do to decide if a sample is at all an indication that one should throw away a hypothesis. Just google hypothesis testing, for example. If you want to decide what the most common colour is, for example, you just need to make lots of tests, then decide if your results are significant enough to discard the hypothesis that all colours are equally likely. So also google significance testing.

Or you could call the manufacturers and ask them.

About the only error I can see is that you attempted to make a judgement about something from a way too small sample. Though you should make it clear if you mean that you want to think about one particular packet, or just a packet in general. And if you want to work out a 'standard deviation' then you need a numerical random variable: the most common colour isn't something that even has a standard deviation. The number of purple M&Ms in a packet is a random variable that has a standard deviation.

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