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A frequency distribution curve is a type of descriptive statistics depicted as a graph that demonstrates the frequency of a given variable's occurrence, where x represents some measure of the variable's occurrence and y represents the number of cases at each frequency. With very large populations, a frequency distribution curve is said to resemble the statistical ideal of a bell curve and assumes the properties of a normal distribution. The bell curve — also known as a normal curve — is aptly named. It resembles a rounded bell with symmetrical ends tapering down and out toward a zero frequency at the x-axis. The bell curve is bisected by the idealized identical mean (μ), median and mode of all the measured data, with half of each graph on either side.
When a sample frequency distribution curve is assumed to possess the properties of an ideal bell curve, then aspects of the population under study can be assumed as well. In addition, standard statistical formulas can give a degree to which such assumptions can be relied upon. With the ideal bell curve, a population's mean, median and mode are all assumed to be equal. Calculation of the standard deviation, σ, then gives a measure of the population data's "spread." In the ideal curve, all but 0.25 percent of a population's total data is found within plus or minus three standard deviations from the mean of the frequency distribution curve, or between μ-3σ and μ+3σ.
While the ideal bell curve differs from a sample frequency distribution curve in a number of ways, it allows some assumptive understanding of both the sample population and even a single measurement's location within the overall sample population. In an ideal curve, 68 percent of the values for the variable measured in the sample, and presumably in the population, will be within one standard deviation from the mean in either direction, or μ-1σ and μ+1σ. Moving further along the bell curve, values for 95 percent of the sample and the population will be located within plus or minus two standard deviations from the mean, or μ-2σ and μ+2σ. At the very edges of frequency distribution curve, all but 0.25 percent falls within plus or minus three standard deviations. Those rare measurements that lie in the 0.25 percent beyond the measures of three standard deviations are known as outliers and are often removed from data when inferential calculations take place.
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