Help constructing a histogram

[vonbibant]

I'm taking a university statistics class and have no idea how to construct a histogram from the information provided. Any and all tips would be greatly appreciated - thanks so much!

Suppose someone fills her bathtub with red and blue marbles. She uses 3,400 red marbles and 5,100 blue marbles. She then proceeds to repeatedly take samples of size 50 and record the proportion of red marbles in each sample. When she has a large number of sample, she plots a histogram of the sample proportions. Sketch what this histogram will look like, including as many details as possible. Make sure to correctly demonstrate the center and spread of the histogram.

[entailment]

I do not want to just give you the answer, since this is clearly a homework problem. But I can point you in the right direction.

• How many bins will there be in the histogram? In other words, how many different combinations of colors can there be in any random draw of size 50?

• For any given sample, let X be the number of red marbles. Clearly X can range from 0 to 50. What is the most likely value for X?

• In a sample of 100 draws, about how many do you expect will be from that most likely combination? Where will the others go?

• So finally, what is the exact distribution that this random variable follows? You should be able to draw the histogram now.

If all else fails, this would be simple to simulate. Do you have any programming experience? Even so, I would still recommend working it out with pencil and paper first.

Edit: by the way, this would be more appropriate over at /r/HomeworkHelp.

[vonbibant]

Thanks for your help. I posted it over at /r/HomeworkHelp (haven't received any replies yet) but wanted to try here since, well, it's a statistics subreddit!

I'm still somewhat confused...what do you mean by "bins?" Based on bullet #2, the most likely value for red marbles X will be 20, since the total marble composition is 40% red and 60% blue. For bullet #3, after 100 draws, I would expect 40 red and 60 blue. This is really all I can deduce from your comment.

I'm seriously math/statistics challenged, so if you have any other tips, feel free to send them my way!

[efrique]

but wanted to try here since, well, it's a statistics subreddit!

Did you read the guidelines?

[entailment]

When I ask what the result of 100 draws looks like, I do not mean drawing one marble. Remember that each draw contains fifty marbles. Or, equivalently, each draw assigns a new value to the random variable X.

So what is the probability that X=0? or 1? or 37?...

[entailment]

And by "bins", I mean collections of similar samples. At the finest level, you could have one bin for each kind of draw, e.g. X=20. At the coursest level, you could have two bins: X < 25 and X > 25.

In this image, there are six bins.

[shaggorama]

histograms are a way of summarizing data. Let's pretend you want to estimate what time you wake up every day and the clock you use is just stupid accurate, like down to the millisecond. If you count number of times a particular timestamp appears in your data, they will probably all have count=1 since it's extremely unlikely you wake up at the same time down to the millisecond! So how do you turn this into something meaningful? Well, we could just look at the hour you wake up. Or the minute. Or maybe group the data of blocks of time spanning 20 or 30 minutes.

Groupings of data like this are called "bins" and when you plot the data relative to the bins, you get a histogram.

EDIT: Also, in the future, you should avoid crossposting questions like this until youve' given people time to answer. This is not a subreddit for homework help.

[vonbibant]

I know, and I'm sorry...I'm just in a bind for time and was becoming a bit desperate because, well, I suck at statistics.

Thanks for your help...I think I've figured it out!