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Example 3 - Find mean deviation about median 3, 9, 5, 3, 12 - Mean deviation about median - Ungrouped

Example 3 - Chapter 15 Class 11 Statistics - Part 2


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Example 3 Find the mean deviation about the median for the following data: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21. Arranging data in ascending order, 3, 3, 4, 5, 7, 9, 10, 12, 18, 19, 21 Here, number of observations = n = 11 (odd). Since n is odd, Median = ( 11 + 1﷮2﷯)th observation M = ( 12﷮2﷯)th observation = 6th observation = 9 Now, we calculate mean deviation about median 3, 3, 4, 5, 7, 9, 10, 12, 18, 19, 21 Median (M) = 9 Mean deviation about median = ﷮﷮ 𝑥𝑖 −M﷯﷯﷮11﷯ M.D.(M) = 3 − 9﷯ + 3 − 9﷯ + 4 − 9﷯ + 5 − 9 ﷯ + 7 − 9﷯ + 9 − 9﷯ ﷮+ 10 − 9﷯ + 12 − 9﷯+ 18 − 9﷯ + 19 − 9﷯ + 21 − 9﷯ ﷯﷯﷮11﷯ = −6﷯ + −6﷯ + −5﷯ + −4 ﷯ + −2﷯ + 0﷯ ﷮+ 1﷯ + 3﷯+ 9﷯ + 10﷯ + 12﷯ ﷯﷯﷮11﷯ = 6 + 6 + 5 + 4 + 2 + 0 + 1 + 3 + 9 + 10 + 12﷯﷮11﷯ = 58﷯﷮11﷯ = 5.27

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.