Statistics - Normal Distribution
A normal distribution is one of the theoretical distributions that has proved to be extremely useful and valuable in the study of statistics. The Gaussian curve gave an accurate picture of the effects of random variation. The nineteenth century mathematician Francis Galton gave the name normal distribution to the curve. It is generally believed that many social and biological measurements are normally distributed.
A normal distribution is a bell-shaped, symmetrical, theoretical distribution based on a mathematical formula rather than on empirical observations. One can observe that the curves often look similar to this theoretical distribution. When the theoretical curve is drawn, the Y axis is sometimes omitted. On the X axis, z scores are used as the unit of measurement for the standardized normal curve, where
z = X – μ/σ
where X = a raw score
μ = the mean of the distribution
σ = the standard deviation of the distribution
there are several other things to note about the normal distribution. The mean, the median, and the mode are the same score – the score on the X axis where the curve peaks. If a line is drawn from the peak to the mean score on the X axis, the area under the curve to the left of the line is half the total area – 50 percent – leaving half of the area to the right of the line. The tails of the curve are asymptotic to the X axis; that is, they never actually cross the axis but continue in both directions indefinitely, with the distance between the curve and the X axis becoming less and less. Although, in theory, the curve never ends, it is convenient to think of the curve as extending from - 3 σ to +3 σ.
Another point about the normal distribution is that the two inflection points in the curve are at exactly -1σ and +1σ. The inflection points are where the curve is the steepest – that is, where the curve changes from bending upward to bending over.
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