The goal of learning statistics is to gain an understanding of how statistics work, and to be able to make correct inferences and predictions from them.
First of all, stats are a great tool for helping you understand something, and for making predictions. The two things that are most valuable in statistics are the mean and the standard deviation. The mean is the average value of a set of data. The mean tells you the mean of a group of observations.
The mean is the average of the entire set of data. The mean shows you what the average is for the entire set of observations, like how many people in a given age group are in the top percentile for a given age. The standard deviation is a measure of how far a set of data deviates from the mean. The standard deviation is calculated by taking the square root of the variance of the set of data.
The difference between the mean and the standard deviation can be used to estimate the size of the set of observations. The mean is the point that would be the same no matter what the set of observations was. The standard deviation tells you how far a set of observations deviates from the mean. The standard deviation allows you to estimate how large the set of observations would be if they were the only thing in the world.
The standard deviation of a set of numbers is a measure of the spread of these numbers. So for example, if you’re watching a race on television, you’d probably prefer to see a lot of cars, more than a few people, and very few horses. A standard deviation of these numbers gives you a sense of how spread out the set of numbers is. It’s a good way to judge the variability of a set of numbers.
I would argue that the goal is to use standard deviations to gauge the variance of a set of numbers, not the number of observations. Why do we care about standard deviations then? Well, as we saw with the movie Titanic, a standard deviation of the ship’s speed is about 15 miles per hour.
The goal of statistics is to tell you how spread out the set of numbers is. And the standard deviation of the speeds is 15 miles per hour. This is a useful concept, because it tells you how many standard deviations from the mean the set of numbers is. For example, if the set of numbers were normally distributed with a mean of zero and standard deviation of one, then the standard deviation of the set of numbers would be one.
The standard deviation of the set of numbers is the standard deviation divided by the mean. This can be thought of as the “width” or “extent” of the set of numbers. So the standard deviation of the set of numbers is the average of the standard deviations of the set of numbers.
The standard deviation of the set of numbers is how far away, in absolute terms, the set of numbers is from the mean. The standard deviation of the set of numbers is how extreme (in absolute terms) a set of numbers is. For example, the standard deviation of the set of numbers is twice the standard deviation of the set of numbers. So the standard deviation of the set of numbers is the square root of the standard deviation of the set of numbers.
The standard deviation of the set of numbers is the same size as the set of numbers.
