Dice throw, avg.,standard deviation

In summary, dice throw refers to the act of rolling a die or multiple dice in a game or experiment. The average of a dice throw refers to the expected or most likely outcome when rolling the dice. The average for multiple dice throws is calculated by adding up all the possible outcomes and dividing by the total number of throws. Standard deviation is a measure of how spread out the outcomes of a dice throw are from the average. To calculate the standard deviation for dice throws, you would first find the average, subtract it from each outcome, square the differences, add them together, divide by the total number of throws, and then take the square root of the result.
  • #1
Pushoam
962
52

Homework Statement


upload_2017-9-11_16-42-6.png


Homework Equations

The Attempt at a Solution


Let's denote the result of the throw by the variable x.
## <x> = Σ_i P_i x_i , i = 1,2,3,...,6.
\\= \frac{1+2+3+4+5+6}{6}
\\<x^2> = \frac{1^2+2^2+3^2+4^2+5^2+6^2}{6}
\\σ_x = \sqrt{<x^2> - <x>^2} ##
Is this correct?
 
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  • #2
Your formulas appear to be correct.
you should get a standard deviation of the form: ##\sigma_x \approx ## *.**7825.
 

FAQ: Dice throw, avg.,standard deviation

1. What is meant by "dice throw" in this context?

Dice throw refers to the act of rolling a die or multiple dice in a game or experiment.

2. What does "average" mean when talking about dice throws?

The average of a dice throw refers to the expected or most likely outcome when rolling the dice. For example, the average of a single die throw is 3.5 since there are six possible outcomes (1, 2, 3, 4, 5, 6) and each outcome has an equal chance of occurring.

3. How is the average calculated for multiple dice throws?

The average for multiple dice throws is calculated by adding up all the possible outcomes and dividing by the total number of throws. For example, if you roll two dice, the possible outcomes are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. To calculate the average, you would add all these numbers and divide by 11 (since there are 11 possible outcomes).

4. What does "standard deviation" mean when throwing dice?

Standard deviation is a measure of how spread out the outcomes of a dice throw are from the average. A high standard deviation means that the outcomes are more spread out, while a low standard deviation means that the outcomes are closer to the average.

5. How is standard deviation calculated for dice throws?

To calculate the standard deviation for dice throws, you would first find the average and then subtract it from each outcome. Then, you would square each of these differences, add them together, and divide by the total number of throws. Finally, you would take the square root of this number to get the standard deviation.

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