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<br />curve is an unlikely occurrence and is used here for illustrative purposes <br /> <br />only. The simplified graph, shown on Figure V-10, has been further <br /> <br />distorted to demonstrate the principles discussed above. Note thst, by <br /> <br />definition, frequencies range from zero to one. This figure should not, <br /> <br />therefore, be construed to represent a realistic situation. It does, <br /> <br />however, serve the intended purpose. The area under the curve is <br /> <br />determined by three methods: by direct integration, by the frequency <br /> <br />interval calculation method, and by directly computing the area from <br /> <br />rectangles. Examples follow: <br /> <br />x-Value <br />Summation <br /> <br />(1) <br /> <br />o <br /> <br />2 <br /> <br />4 <br /> <br />6 <br /> <br />8 <br /> <br />a. <br /> <br />Direct Inteiration: <br />y - f(x) - bx+a <br /> - 500x +1000 <br />I: (500x + 1000)dx-[250x2+1OOOx] <br />_[250(8)2 + 1000]8 - 0 <br />Area - 16000 + 8000 - ~ <br />Freauencv Interval Calculation Method: <br />Interval Y-Value Average '-. (2) x (4) TOTAL <br />(2) (3) (4) (5) (6) <br /> 1000 24000 <br />2 1500 3000 21000 <br /> 2000 <br />2 2500 5000 16000 <br /> 3000 <br />2 3500 7000 9000 <br /> 4000 <br />2 4500 9000 0 <br /> 5000 <br /> <br />b. <br /> <br />Area - 24.000 <br /> <br />V-56 <br />