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AP EAMCET202419 May 2024Evening ShiftMathematicsStatisticsActual

If m and M denote the mean deviations about mean and about median respectively of the data 20,5.15,2,7,3,11 then the mean deviation about the mean of m and M is

Options

  1. A1 7
  2. B38 7
  3. C36 7
  4. D37 7

Correct answer

A. 1 7

Step-by-step solution

Since, mean of the given data x = 20+5+15+2+7+3+11 7 =9 Now, mean deviation about mean aligned = & |9-20|+|9-5|+|9-15|+|9-2|+|9-7|+|9-3|+|9-11| 7 = 38 7 =m aligned Since, Median = ( 7+1 2 )^ th term =4^ th term =7 (after ascending order) Now, mean deviation about median = |20-7|+|5-7|+|15-7|+|2-7|+|7-7|+|3-7|+|11-7| 7 = 36 7 =M Let x ^ = 1 2 ( 36 7 + 38 7 )= 74 2 7 = 37 7 So, mean deviation about mean = 1 2 ( | 37 7 - 38 7 |+ | 37 7 - 36 7 | )= 1 2 ( 2 7 )= 1 7 .

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