The blue (left-most) distribution has a mean of −3 and a standard deviation of 0.5, the distribution in red (the middle distribution) has a mean of 0 and a standard deviation of 1, and the black (right-most) distribution has a mean of 2 and a standard deviation of 3. Figure 4.1 shows three normal distributions. Normal distributions can differ in their means and in their standard deviations. Strictly speaking, it is not correct to talk about “the normal distribution” since there are many normal distributions. It is also called the “Gaussian curve” of Gaussian distribution after the mathematician Karl Friedrich Gauss. It is sometimes called the “bell curve,” although the tonal qualities of such a bell would be less than pleasing. The normal distribution is the most important and most widely used distribution in statistics. Moving forward, we now turn our attention to how scores within a distribution are related to one another, how to precisely describe a score’s location within the distribution, and how to compare scores from different distributions. These simple tools, and the principles behind them, will help you interpret information presented to you and understand the basics of a variable. We now understand how to describe and present our data visually and numerically.
