central limit theorem: The theorem that states: If the sum of independent identically distributed random variables has a finite variance, then it will be (approximately) normally distributed.normal probability plot: a graphical technique used to assess whether or not a data set is approximately normally distributed.The data are plotted against a theoretical normal distribution in such a way that, if the data is normal, the points should form an approximate straight line. A normal probability plot is another method used to assess normality.If the graph is approximately bell-shaped and symmetric about the mean, you can usually assume normality. Just by looking at a probability histogram, you can tell if it is normal by looking at its shape.The occurrence of the normal distribution in practical problems can be loosely classified into three categories: exactly normal distributions, approximately normal distributions, and distributions modeled as normal.If we had instead tossed a coin four times in many trials and created a relative frequency histogram, we would have gotten a graph that looks similar to this one, but it would be unlikely that it would be perfectly symmetric. Notice that this particular probability histogram is symmetric, and resembles the normal distribution. Then, rectangles of equal widths should be drawn according to their corresponding probabilities. Regular histograms have a \text: in this case, 0, 1, 2, 3, and 4. Histograms break the range of values in classes, and display only the count or percent of the observations that fall into each class. Visual graphs, such as histograms, help one to easily see a few very important characteristics about the data, such as its overall pattern, striking deviations from that pattern, and its shape, center, and spread.Ī histogram is particularly useful when there is a large number of observations. When examining data, it is often best to create a graphical representation of the distribution. discrete random variable: obtained by counting values for which there are no in-between values, such as the integers 0, 1, 2, ….
As in all probability distributions, the probabilities of all the outcomes must add up to one.By looking at a probability histogram, one can visually see if it follows a certain distribution, such as the normal distribution.In a probability histogram, the height of each bar showsthe true probability of each outcome if there were to be a very large number of trials (not the actual relative frequencies determined by actually conducting an experiment ).