Statistics: Pattern present in dice data?

[jdawg]

Homework Statement

I generated data for a dice experiment. For the first case, two dies were rolled and the minimum number and the sum were recorded. For the other cases with three, four, and five dies, the minimum and sum were also recorded. I attached a picture of the tables with my data and the calculated average, median, range, and variance.

Are there any patterns present in the calculated average, median, range, and variance?

I also attached a picture of a graph I made in excel.

Are there are any patterns present when you plot the min vs the sum? I would think not since dice rolling is random? But the way my professor asked the question makes me think there should be one appearing somewhere.

In the graph I attached, if you subtract the amount of data points in the second row from the first row, you get the amount of data points in the fifth row. Subtracting the third from the first you get the fourth row. But is this a pattern?

Thanks for any help!

 

[Simon Bridge]

Are there any patterns present in the calculated average, median, range, and variance?

I also attached a picture of a graph I made in excel.

Are there are any patterns present when you plot the min vs the sum? I would think not since dice rolling is random? But the way my professor asked the question makes me think there should be one appearing somewhere.

... have you tried looking at the graphs to see?
You should also think about your data to see if it makes sense too.

Lets make sure I understand - you rolled n regular fair 6 sided dice 20 times, recording the value L of the lowest die and also the sum S of the dice rolled.

Although the dice rolled are random, they cannot just come up with any old number ...

The lowest L possible is L=1
How does the probability that L=1 vary with n?

The highest L possible is L=6.
Looking at your data, you don't have a 6 there - why do you think that is?
If you did have one, what are the possible values of S (say for n=2)?

 

[jdawg]

I did look at the graph, but I didn't really see any pattern... Yes that's correct. Are you saying some of my calculated values in the last table are incorrect?

I'm not sure if I understand the direction you're trying to steer me in.

 

[Simon Bridge]

I did look at the graph, but I didn't really see any pattern...

OK. So describe the graph to me.
Looking at the n=2 graph of S vs L you supplied, what happens to the number of data points as L increases?
What is the trend there ... as L increases S gets bigger/smaller/stays the same (pick one).

Are you saying some of my calculated values in the last table are incorrect?

No. I am directing your attention to patterns.

I'm not sure if I understand the direction you're trying to steer me in.

Have you tried answering the questions?
If you will not answer questions nobody can help you.
If you will not follow suggestions nobody can help you.

 

[jdawg]

Oh, it looks like the number of data points decreases for the most part as you move along the positive x direction. And it looks like the sum is a lot higher when you have a larger minimum? I hope I understood your question correctly.

 

[Simon Bridge]

Oh, it looks like the number of data points decreases for the most part as you move along the positive x direction. And it looks like the sum is a lot higher when you have a larger minimum? I hope I understood your question correctly.

Well done - are those not patterns?

How about my other questions - from post #2?

Lets make sure I understand - you rolled n regular fair 6 sided dice 20 times, recording the value L of the lowest die and also the sum S of the dice rolled.
(* Do I understand you correctly?)

Although the dice rolled are random, they cannot just come up with any old number ...

The lowest L possible is L=1
* Using your understanding of probability and statistics: how would the probability that L=1 vary with n?
(Does it increase, decrease, or remain unchanged, as n gets bigger?)
* Does the data support this conclusion?

The highest L possible is L=6.
* Looking at your data, how many times do you see L=6 (for any n)?
* Using your understanding of probability and statistics: why do you think that is?
* If you did have one L=6, what are the possible values of S (say for n=2)?
* Compare with the possible values of S for L=5 (say for n=2)

I'm trying to get your brain started hunting patterns - the human brain is good at pattern recognition, it is difficult to stop it doing this.
So it is a genuine puzzle when you say you do not see any patterns in the graphs at all.

 

[jdawg]

Lets make sure I understand - you rolled n regular fair 6 sided dice 20 times, recording the value L of the lowest die and also the sum S of the dice rolled.
(* Do I understand you correctly?)

Yes, exactly!

The lowest L possible is L=1
* Using your understanding of probability and statistics: how would the probability that L=1 vary with n?
(Does it increase, decrease, or remain unchanged, as n gets bigger?)
* Does the data support this conclusion?

Well, I would think that as the number of dice are increased, there would be a smaller chance of rolling a 1 for the minimum. But my data suggests otherwise. It looks like I have a greater amount of 1's for the minimum as n gets bigger.

The highest L possible is L=6.
* Looking at your data, how many times do you see L=6 (for any n)?
* Using your understanding of probability and statistics: why do you think that is?
* If you did have one L=6, what are the possible values of S (say for n=2)?
* Compare with the possible values of S for L=5 (say for n=2)

I don't see any L's with a value of 6. I guess this is because you would have to roll all 6's to get 6 as a minimum value. If L = 6 for the 2 die case, you could only have 12 as a value for the sum. If L = 5, then the only possible sum values would be 10 or 11.

I'm trying to get your brain started hunting patterns - the human brain is good at pattern recognition, it is difficult to stop it doing this.
So it is a genuine puzzle when you say you do not see any patterns in the graphs at all.

Haha it might be because originally when I plotted the graph I connected all the dots and saw that the line connecting them was all over the place. That made me think it was random. I guess for this experiment it doesn't make sense to connect the data points.

 

[Simon Bridge]

Well, I would think that as the number of dice are increased, there would be a smaller chance of rolling a 1 for the minimum. But my data suggests otherwise. It looks like I have a greater amount of 1's for the minimum as n gets bigger.

Good observations.
The experiment disagrees with your understanding... which is to say that your understanding does not correspond to reality in this case.
This means you need to revisit your understanding of probability and statistics.
To get L=1, you need n dice to roll at least one 1.
For n=1, the probability of at least one 1 is 1/6
For n=2, the probability is what?

I don't see any L's with a value of 6. I guess this is because you would have to roll all 6's to get 6 as a minimum value. If L = 6 for the 2 die case, you could only have 12 as a value for the sum. If L = 5, then the only possible sum values would be 10 or 11.

... well done. How does that compare with your data?

You should be starting to see what is meant by patterns now.
The next step is to compare the n=2 plot with the other ones.

 

[jdawg]

Wow I can't believe I messed that up. Thanks so much for your help!