In other words, a value in the 95th percentile is greater than ?95\%? of the data. The nth percentile is the value such that n percent of the values lie below it. We look a lot at percentiles within a normal distribution. Or if we wanted to know how much of our data will lie between one and two standard deviations from the mean, we can say that it’s ?95\%-68\%=27\%?. For example, since total area is ?100\%?, and the data within three standard deviations is ?99.7\%?, that means that we’ll always have ?0.3\%? of the data in a normal distribution that lies outside three standard deviations from the mean. We can show that ?68\%? of the data will fall within ?1? standard deviation of the mean, that within ?2? full standard deviations of the mean we’ll have ?95\%? of the data, and that within ?3? full standard deviations from the mean we’ll have ?97.7\%? of the data.Īnd we can draw all kinds of conclusions based on this information, and the fact that the all the area under the graph represents ?100\%? of the data.
