A frequency distribution curve is a graph showing the frequency of occurrence of a variable. The ideal bell curve is symmetrical and has the mean, median, and mode equal. Standard deviation provides a measure of the “spread” of population data. The curve allows for understanding of both the sample population and the position of an individual measurement. Outliers are rare measurements that are often removed from data.
A frequency distribution curve is a type of descriptive statistic represented as a graph demonstrating the frequency of occurrence of a given variable, where x represents a measure of the occurrence of the variable 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 take on the properties of a normal distribution. The bell curve, also known as the normal curve, is aptly named. It resembles a rounded bell with symmetrical ends that taper down and out towards a zero frequency on the x-axis. The bell curve is bisected by the idealized identical mean (μ), median, and mode of all 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, aspects of the population under study can also be assumed. Furthermore, standard statistical formulas can provide a degree to which such assumptions can be relied upon. With the ideal bell curve, the mean, median, and mode of a population are all assumed to be equal. Calculation of the standard deviation, , then provides a measure of the “spread” of population data. In the ideal curve, all but 0.25 percent of the total data for a population is within plus or minus three standard deviations of 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 for a presumptive understanding of both the sample population and also the position of an individual measurement within the overall sample population. In an ideal curve, 68% of the values for the measured variable in the sample, and presumably in the population, will be within one standard deviation of the mean in both directions, or μ-1σ and μ+1σ. Moving further along the bell curve, the values for 95% of the sample and population will be within plus or minus two standard deviations of the mean, or μ-2σ and μ+2σ. At the edge of the frequency distribution curve, everything but 0.25 percent falls within plus or minus three standard deviations. Those rare measurements that are within 0.25 percent of measurements by three standard deviations are known as outliers, and are often removed from the data when inferential calculations occur.
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