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Ex 15.1
Last updated at May 29, 2018 by Teachoo
Ex 15.1, 3 Find the mean deviation about the median for the data. 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17 Arranging data in ascending order, 10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18 Here, n = number of observations = 12 (even) Since n is even Median = đīˇŽ2īˇ¯īˇ¯īˇŽđĄâđđđ đđđŖđđĄđđđ + đīˇŽ2 + 1īˇ¯īˇŽđĄâđđđ đđđŖđđĄđđđīˇŽ2 M = 12īˇŽ2īˇ¯īˇ¯īˇŽđĄâđđđ đđđŖđđĄđđđ + 12īˇŽ2 + 1īˇ¯īˇŽđĄâđđđ đđđŖđđĄđđđīˇŽ2 M = 6īˇŽđĄâđđđ đđđŖđđĄđđđ + 7īˇŽđĄâđđđ đđđŖđđĄđđđīˇŽ2 M = 13 + 14īˇŽ2 = 27īˇŽ2 = 13.5 Thus, for 10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18 Median = 13.5 Mean deviation about median = īˇŽīˇŽ đĨđ âMīˇ¯īˇ¯īˇŽ12 = 10 â 13.5 + 11 â 13.5 + 11 â 13.5 + 12 â 13.5 + 13 â 13.5+ 13 â 13.5īˇ¯īˇŽ+ 14 â 13.5 + 16 â 13.5 + 16 â 13.5 + 17 â 13.5 + 17 â 13.5+ 18 â 13.5īˇ¯īˇ¯īˇ¯īˇŽ12 = â3.5 + â2.5 + â2.5 + â1.5 + â0.5 + â0.5īˇ¯īˇŽ+ 0.5 + 2.5 + 2.5+ 3.5 + 3.5 + 4.5 īˇ¯īˇ¯īˇŽ12 = 3.5 + 2.5 + 2.5 + 1.5 + 0.5 + 0.5 + 0.5 + 2.5 + 2.5 + 3.5 + 3.5 + 4.5īˇŽ12 = 28īˇŽ12 = 2.33