Example: Converting A Normal Distribution To A Standard Normal Distribution Where X is the variable for the original normal distribution and Z is the variable for the standard normal distribution. This leaves the mean at 0, but changes the standard deviation from S to 1. Then, we divide every data point by the standard deviation S of the distribution. This changes the mean from M to 0, but leaves the standard deviation unchanged. To do this, we first subtract the value of the mean M of the distribution from every data point. However, we first need to convert the data to a standard normal distribution, with a mean of 0 and a standard deviation of 1. We can use a standard normal table to find the percentile rank for any data value from a normal distribution. This is because the mean of a normal distribution is also the median, and thus it is the 50 th percentile.Ī standard normal distribution has a mean of 0 and a standard deviation of 1. When a data point in a normal distribution is above the mean, we know that it is above the 50 th percentile. 1, 2, Or 3 Standard Deviations Above The Mean In this article, we’ll talk about standard deviations above the mean and what it means, along with examples to make the concept clear. Of course, converting to a standard normal distribution makes it easier for us to use a standard normal table (with z scores) to find percentiles or to compare normal distributions. On the other hand, being 1, 2, or 3 standard deviations below the mean gives us the 15.9 th, 2.3 rd, and 0.1st percentiles. So, what do standard deviations above or below the mean tell us? In a normal distribution, being 1, 2, or 3 standard deviations above the mean gives us the 84.1 st, 97.7 th, and 99.9 th percentiles. We can also figure out how “extreme” a data point is by calculating how many standard deviations above or below the mean it is. Mean and standard deviation are both used to help describe data sets, especially ones that follow a normal distribution.