One way to get rid of the randomness of the distribution is to use the mean. But, with the right approach, you can expect your observations to have a mean that is somewhere in between.

This is the idea behind the ________ range. If your observations are close to the mean, then you can more or less eliminate the influence of randomness. But when your observations are not close to the mean, then the influence of randomness is more pronounced so you will need to use a different approach.

________ represents the standard deviation, or “spread,” of a distribution. A standard deviation is the spread of the distribution over a group of numbers. By taking a collection of numbers and finding the standard deviation of that set of numbers, you can find how much the group deviates from the mean.

If you have a set of data that is not close to the mean, then the standard deviation must be much bigger than the mean. Similarly, if your measurements are not close to the mean, then the standard deviation of the set of numbers must be much smaller than the mean. The standard deviation is a measure of the spread of the data.

Standard deviation is just another way of saying variance.

You can think of a standard deviation as the deviation of the data from the mean. The idea is that if you have a set of numbers that are all close to the mean, then the standard deviation of that set of numbers must be very large. And vice versa, if your set of numbers is all very large then the standard deviation must be very small.

This is really important because the concept of standard deviation allows us to see how much the data is to the left and right of the mean. In a normal distribution the average of the data is not much smaller than the mean, so the standard deviation of the data is very large. But if the data looks like a bell curve, then the standard deviation of the data is very small. The standard deviation is a very useful way of finding out how far off of the mean something is.

The idea of a standard deviation is not particularly new. It was one of the first things that we learned as students at the University of Waterloo. It was also one of the first things that we learned when we started studying statistics.

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