Ex 13.1, 3 - Chapter 13 Class 11 Statistics
Last updated at April 16, 2024 by Teachoo
Last updated at April 16, 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 = ๐๏ทฎ2๏ทฏ๏ทฏ๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐ + ๐๏ทฎ2๏ทฏ + 1๏ทฏ๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐๏ทฎ2๏ทฏ M = 12๏ทฎ2๏ทฏ๏ทฏ๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐ + 12๏ทฎ2๏ทฏ + 1๏ทฏ๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐๏ทฎ2๏ทฏ M = 6๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐ + 7๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐๏ทฎ2๏ทฏ M = 13 + 14๏ทฎ2๏ทฏ = 27๏ทฎ2๏ทฏ = 13.5 Thus, for 10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18 Median = 13.5 Mean deviation about median = ๏ทฎ๏ทฎ ๐ฅ๐ โM๏ทฏ๏ทฏ๏ทฎ12๏ทฏ = 10 โ 13.5๏ทฏ + 11 โ 13.5๏ทฏ + 11 โ 13.5๏ทฏ + 12 โ 13.5๏ทฏ + 13 โ 13.5๏ทฏ+ 13 โ 13.5๏ทฏ๏ทฎ+ 14 โ 13.5๏ทฏ + 16 โ 13.5๏ทฏ + 16 โ 13.5๏ทฏ + 17 โ 13.5๏ทฏ + 17 โ 13.5๏ทฏ+ 18 โ 13.5๏ทฏ๏ทฏ๏ทฏ๏ทฎ12๏ทฏ = โ3.5๏ทฏ + โ2.5๏ทฏ + โ2.5๏ทฏ + โ1.5๏ทฏ + โ0.5๏ทฏ + โ0.5๏ทฏ๏ทฎ+ 0.5๏ทฏ + 2.5๏ทฏ + 2.5๏ทฏ+ 3.5๏ทฏ + 3.5๏ทฏ + 4.5๏ทฏ ๏ทฏ๏ทฏ๏ทฎ12๏ทฏ = 3.5 + 2.5 + 2.5 + 1.5 + 0.5 + 0.5 + 0.5 + 2.5 + 2.5 + 3.5 + 3.5 + 4.5๏ทฎ12๏ทฏ = 28๏ทฎ12๏ทฏ = 2.33