Value of Statistics
 Statistical Analysis | The Normal Distributions
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The Normal Distributions One of the most important frequency distributions in statistics is the normal distribution. Many statistical procedures are based on knowledge of this distribution and assume it is the underlying distribution of the population sampled. Its appearance is that of symmetrical bell-shaped curve with the tails of the curve extending infinitely in both positive and negative directions. See figure 2.
Figure 2 Normal distribution with equal means and unequal standard deviations. Numbers on x-axis refer to standard deviations units. Note that all three curves are symmetrical about the mean. Under such a curve the proportion of the area between any two points is completely determined by the mean, x, and the standard deviation, s. For example, approximately 2/3 (68.26%) of the entire area under the curve is contained between ±1 standard deviations from the mean (See figure 2). About 98% of the total area lies between ± 2 standard deviations from the mean. 50% of the area lies between ª ± 0.65s, and 95% of the area lies between ª ± 1.96s. Figure 3. A normal distribution showing the proportion of area lying within one and two standard deviations. For more on normal curves and standard distributions, areas under the curve link
to: http://www.psychstat.smsu.edu/introbook/sbk11m.htm |
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