![]() ![]() One half of the data points lie to the left of μ and the remaining half lie to the right, no matter how spread out they are. One of the distinctions of the normal distribution is related to its symmetry. It is possible because the family of normal distributions are related by the way the data points are arranged under portions of the curve. We can do this by performing some simple mathematical alterations to each data point. It is to our advantage to somehow standardize all of these curves so we only need to refer to one. We will ultimately use the curve as a frequency distribution to plot outcomes on the abscissa, so we can see the probability of their occurrence on the ordinate. We see that the normal distribution is actually a collection of bell-shaped curves, depending on μ and σ. As σ gets larger the curve gets shallow and wide. If the standard deviation is σ small, the curve is narrow and tall. Figure 9-1 shows that it has a graceful bell shape, and thus is sometimes referred to as the bell curve.įIGURE 9-3 In a normal distribution the mode = mean = median = 50th percentile = μ. The famous mathematician Carl Friedrich Gauss expounded on this distribution, so it also became known as the Gaussian distribution. This is called a normal distribution, since de Moivre attributed this pattern to the orderliness of the natural world. The ends tailed off toward the abscissa because the values farthest from the mean value were less likely to occur. The data points were distributed equally on either side of the mean. When he plotted the values in a frequency distribution, the result was a unimodal and symmetric curve. He demonstrated that the values of a variable in a sample would be distributed around the average value. He realized that to use samples to represent much larger populations, as Jacob Bernoulli had suggested, a pattern must emerge from the data. The normal distribution was originally presented by the French mathematician Abraham de Moivre (1667–1754). For this reason, it is used as a prototype to demonstrate how the process of inferential statistics works. It is also one of the most commonly used distributions in statistics because it portrays the relative frequency with which a particular outcome could occur in many types of situations. There is a distinct type of frequency distribution that occurs naturally in many types of biologic data, especially variables that follow a continuous or interval scale. The process begins with the bell curve, the main purpose of which is to indicate not accuracy but error. ![]()
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