Ex 13.1

Chapter 13 Class 11 Statistics
Serial order wise

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Transcript

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๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐ + ๐๏ทฎ2๏ทฏ + 1๏ทฏ๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐๏ทฎ2๏ทฏ M = 12๏ทฎ2๏ทฏ๏ทฏ๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐ + 12๏ทฎ2๏ทฏ + 1๏ทฏ๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐๏ทฎ2๏ทฏ M = 6๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐ + 7๏ทฎ๐กโ๏ทฏ๐๐๐ ๐๐๐ฃ๐๐ก๐๐๐๏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 ๐ฅ๐ โM๏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 = โ3.5๏ทฏ + โ2.5๏ทฏ + โ2.5๏ทฏ + โ1.5๏ทฏ + โ0.5๏ทฏ + โ0.5๏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