In comparing a uniform distribution with a normal distribution where both distributions have the same mean and the same range, explain which distribution will have the larger standard deviation
What will be an ideal response?
A picture of this situation would show a larger area of the uniform distribution farther away from the mean. In the normal distribution, the majority of the distribution is close to the mean and a much smaller proportion is near the edges. As the empirical rule says, about 68 percent should be within one standard deviation of the mean. In the uniform distribution this percentage will be lower (about 58 percent). Further the standard deviation of the normal distribution can be approximated using the 6-sigma rule of thumb for the range, meaning that the standard deviation is approximately 1/6 of the range. In the uniform distribution the standard deviation is (range)/3.46, where 3.46 is the square root of 12. All of which gives a larger standard deviation to the uniform distribution.
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