Data are collected for dependent variable many time in statistics where it replaces a bunch of numbers for the independent variable x. An example is the fuel consumption observation could be looked unto as the function of the engine speed. Mean while the load is kept constant. So that you get a small variance in y many repeated test are done at the value of x. The cost of testing might become prohibitive. Arguably reliable predictions of variance can be found by the use of pooled variance formula. Just after repeating every test at a certain x for a minimal time. To get estimating variance one ought to use pooled variance. Having many different samples taken in a varying circumstances. The mean may differ between samples though the true variance which is also referred to as equivalent precision is thought to be constant. The square root of pooled variance formula is referred to as pooled standard deviation.

When a bulk collection of numbers is together, like in a census, most likely we are not so much touched by the number. It's more likely that you would be more happy with the meridian than the total number combined. A die has to be rolled and if an odd number be the result we get to win with the same number. If even number turns up we lose with the same margin. An example is when 2 arises we lose with 2 and when we toss and get 3 we win 3.The program run the results shown is 6.1. The first time we get to run 100 times. Our average profit is -.57. We have already played the game 10,000 times and our average gains are -4949.

One is constantly more concerned by the average value of a set data. An example is where the average data of heights in a team of football is 67.9. At a random variable one can interpret this to be the expected value. Picking one of the footballers let it be denoted by the letter x. The most probable value of x is likely to be 67.9. Frequency interpretation of probability requires further interpretation. It's not predictable for any finite experience for the average results. However it is possible to prove that the outcome is close to x if it's repeated severally. One needs to develop some character of the expected outcome. You get to use these properties and the way of the variance.