This is a standard deviation contest. You have a six sided die with the numbers 1 to 6 written on the faces.
a)In order to have the smallest possible standard deviation what number(s) would have to show up if you rolled the die five times?
b)In order to have the largest possible standard deviation what number(s) would have to show up if you rolled the die five times?
c)Redo (a) or (b) if no repeats allowed. You ignore a repeated number and roll again
a) to have no standard deviation at all would be the smallest possible. SD = 0. I think the same number would have to come up 5 times.
b)You would want the widest range of numbers. I am thinking 1's and 6's
To answer these questions, we first need to understand what standard deviation is. Standard deviation measures how spread out the values in a dataset are from their average. In the context of rolling a six-sided die, the values would be the numbers that show up after rolling the die, and the dataset would consist of these values.
a) In order to have the smallest possible standard deviation, we would want the numbers to be as close together as possible. Rolling the same number every time would result in the smallest deviation. Therefore, if you rolled the die five times, the number that would have to show up every time to minimize the standard deviation would be any single number between 1 and 6.
b) In order to have the largest possible standard deviation, we would want the numbers to be as spread out as possible. This implies that different numbers should show up with equal frequency. To achieve this, you could roll the die in such a way that each number shows up once. This would result in the largest deviation. Therefore, if you rolled the die five times, all the numbers from 1 to 6 would have to show up once each to maximize the standard deviation.
c) If no repeats are allowed and you ignore a repeated number and roll again, the answers for (a) and (b) would be different.
- For the smallest possible standard deviation: In this case, you would want the numbers to be as close together as possible without repeating any. Therefore, if you roll the die five times, the numbers would have to be chosen alternately from 1 to 6. For example, the sequence could be 1, 2, 3, 4, 5, with no repetition. This would result in the smallest deviation.
- For the largest possible standard deviation: Following the same principle, you would want the numbers to be as spread out as possible without repeating any. Therefore, if you roll the die five times, the numbers would have to be chosen in such a way that each number shows up once, but no repetition occurs. For example, the sequence could be 1, 3, 5, 2, 4, with no repetition. This would result in the largest deviation.
Remember, these are hypothetical scenarios, and the actual results of rolling a die can vary.