Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In statistics, many times, data is collected for a dependent variable, y, over a range of values for the independent variable, x. For example, the observation of fuel consumption might be studied as a function of engine speed while the engine load is held constant. If, in order to achieve a small variance in y, numerous repeated tests are required at each value of x, the expense of testing may become prohibitive. Reasonable estimates of variance can be determined by using the principle of pooled variance after repeating each test at a particular x only a few times. Pooled variance is a method for estimating variance given several different samples taken in different circumstances where the mean may vary between samples but the true variance (equivalently, precision) is assumed to remain the same. It is calculated by s_p^2=frac{sum_{i=1}^k((n_i - 1)s_i^2)}{sum_{i=1}^k(n_i - 1)} or with simpler notation, s_p^2=frac{(n_1 - 1)s_1^2+(n_2 - 1)s_2^2+cdots+(n_k - 1)s_k^2}{n_1+n_2+cdots+n_k - k}