Ex 13.1, 3 - Chapter 13 Class 11 Statistics
Last updated at May 7, 2024 by Teachoo
Last updated at May 7, 2024 by Teachoo
Ex 13.1, 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¯īˇŽđĄâīˇ¯đđđ đđđŖđđĄđđđ + đīˇŽ2īˇ¯ + 1īˇ¯īˇŽđĄâīˇ¯đđđ đđđŖđđĄđđđīˇŽ2īˇ¯ M = 12īˇŽ2īˇ¯īˇ¯īˇŽđĄâīˇ¯đđđ đđđŖđđĄđđđ + 12īˇŽ2īˇ¯ + 1īˇ¯īˇŽđĄâīˇ¯đđđ đđđŖđđĄđđđīˇŽ2īˇ¯ M = 6īˇŽđĄâīˇ¯đđđ đđđŖđđĄđđđ + 7īˇŽđĄâīˇ¯đđđ đđđŖđđĄđđđīˇŽ2īˇ¯ M = 13 + 14īˇŽ2īˇ¯ = 27īˇŽ2īˇ¯ = 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¯īˇŽ12īˇ¯ = 10 â 13.5īˇ¯ + 11 â 13.5īˇ¯ + 11 â 13.5īˇ¯ + 12 â 13.5īˇ¯ + 13 â 13.5īˇ¯+ 13 â 13.5īˇ¯īˇŽ+ 14 â 13.5īˇ¯ + 16 â 13.5īˇ¯ + 16 â 13.5īˇ¯ + 17 â 13.5īˇ¯ + 17 â 13.5īˇ¯+ 18 â 13.5īˇ¯īˇ¯īˇ¯īˇŽ12īˇ¯ = â3.5īˇ¯ + â2.5īˇ¯ + â2.5īˇ¯ + â1.5īˇ¯ + â0.5īˇ¯ + â0.5īˇ¯īˇŽ+ 0.5īˇ¯ + 2.5īˇ¯ + 2.5īˇ¯+ 3.5īˇ¯ + 3.5īˇ¯ + 4.5īˇ¯ īˇ¯īˇ¯īˇŽ12īˇ¯ = 3.5 + 2.5 + 2.5 + 1.5 + 0.5 + 0.5 + 0.5 + 2.5 + 2.5 + 3.5 + 3.5 + 4.5īˇŽ12īˇ¯ = 28īˇŽ12īˇ¯ = 2.33