Ex 15.1, 3

Transcript

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 = 𝑛﷮2﷯﷯﷮𝑡ℎ﷯𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + 𝑛﷮2﷯ + 1﷯﷮𝑡ℎ﷯𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛﷮2﷯ M = 12﷮2﷯﷯﷮𝑡ℎ﷯𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + 12﷮2﷯ + 1﷯﷮𝑡ℎ﷯𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛﷮2﷯ M = 6﷮𝑡ℎ﷯𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 + 7﷮𝑡ℎ﷯𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛﷮2﷯ M = 13 + 14﷮2﷯ = 27﷮2﷯ = 13.5 Thus, for 10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18 Median = 13.5 Mean deviation about median = ﷮﷮ 𝑥𝑖 −M﷯﷯﷮12﷯ = 10 − 13.5﷯ + 11 − 13.5﷯ + 11 − 13.5﷯ + 12 − 13.5﷯ + 13 − 13.5﷯+ 13 − 13.5﷯﷮+ 14 − 13.5﷯ + 16 − 13.5﷯ + 16 − 13.5﷯ + 17 − 13.5﷯ + 17 − 13.5﷯+ 18 − 13.5﷯﷯﷯﷮12﷯ = −3.5﷯ + −2.5﷯ + −2.5﷯ + −1.5﷯ + −0.5﷯ + −0.5﷯﷮+ 0.5﷯ + 2.5﷯ + 2.5﷯+ 3.5﷯ + 3.5﷯ + 4.5﷯ ﷯﷯﷮12﷯ = 3.5 + 2.5 + 2.5 + 1.5 + 0.5 + 0.5 + 0.5 + 2.5 + 2.5 + 3.5 + 3.5 + 4.5﷮12﷯ = 28﷮12﷯ = 2.33