| Variance and Standard Deviation |
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Two of the basics statistics terms you'll want to get familiar with are variance and standard deviation. These are used to describe the difference between expected results and actual results. We need to be able to accurately measure and describe these differences to know if our betting strategy has any statistical relevance or significance. The best way to describe the concepts of variance and standard deviation is to use an example. Let's say that we like to grow tomatoes. We grow ten tomatoes and measure the diameter of each and the results are. 2.6, 2.6, 2.8, 3.0, 3.1, 3.2, 3.3, 3.5 , 3.6 and 3.8 inches in diameter. The mean diameter of our tomatoes (found by adding the diameters and dividing by 10) is 3.15. None of our tomatoes is exactly 3.15 inches in diameter, however. They range from 0.55 inches smaller to 0.65 inches larger than that. If we measured each tomato's difference from the mean, we could describe them thus: -0.55, -0.55, -0.35, -0.15, -0.05, 0.05, 0.15, 0.35, 0.45, and 0.65. What then is the average difference? Add and divide by ten? Adding them up gives zero. In fact, adding up all the differences from the mean in a population always equals zero. The negative numbers always balance out the positive numbers when looking at difference from the mean. Inherently that should make some sense even without the math. How then do mathematicians adjust for that to be able to describe difference from the mean in a meaningful way? They get rid of the negative numbers by squaring the difference from the mean before calculating the mean of the differences. That's a mouthful! The differences squared give us the values 0.3025, 0.3025, 0.1225, 0.0225, 0.0025, 0.0025, 0.0225, 0.1225, 0.2025, 0.4225. The mean value of these numbers is 0.1525. This is known as the variance. For our population of tomatoes, the variance from the mean is 0.1525 inches. As we've squared the differences this number does not hold much meaning for us. A more meaningful number would be the square root of the variance. In this case that number is 0.3905 (rounded to 4 digits). That is the standard deviation from the mean for our sample of ten tomatoes.The concept of standard deviation hold quite a lot of significance for us in our application of statistics. So, for review: The variance is the mean of the squares of the individual differences from the sample mean. The standard deviation from the mean is the square root of the variance. Fortunately you can avoid most of the tedium of pounding all of the numbers into you calculator over and over by using a spreadsheet application such as MS EXCEL that will do it for you.
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