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AP EAMCET202420 May 2024Evening ShiftMathematicsStatisticsActual

If the mean deviation about the mean is m and variance is ^2 for the following data, then m+ ^2= array |c|c|c|c|c|c| & 1 & 3 & 5 & 7 & 9 & 4 & 24 & 28 & 16 & 8 array

Options

  1. A8
  2. B7.2
  3. C28 5
  4. D6

Correct answer

D. 6

Step-by-step solution

array |c|c|c|c|c|c| x _ i & f _ i & x _ i f_ i & | x _ i - x | & f _ i | x _ i - x | & x _ i ^ 2 f _ i 1 & 4 & 4 & 4 & 16 & 4 3 & 24 & 72 & 2 & 48 & 216 5 & 28 & 140 & 0 & 0 & 700 7 & 16 & 112 & 2 & 32 & 784 9 & 8 & 72 & 4 & 32 & 648 Total & 80 & 400 & & 128 & 2352 array Mean = x_i f_i f_i = 400 80 =5 Mean deviation =m= f_i |x_i- x | f_i = 128 80 = 8 5 Variance ( ^2 )= x_i^2 f_i f_i -( x )^2= 2352 80 -25= 352 80 = 22 5 Now, m+ ^2= 8 5 + 22 5 = 30 5 =6

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