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AP EAMCET201920 Apr 2019Morning ShiftMathematicsStatisticsActual

If (a₀, a₁, , a₁₁ ) are in an arithmetic progression with common difference (d ), then their mean deviation from their arithmetic mean is

Options

  1. A( 30 11 |d| )
  2. B(2|d| )
  3. C(3|d| )
  4. D(12|d| )

Correct answer

C. (3|d| )

Step-by-step solution

Since, mean of given data is ( aligned x & = a₀+a₁+a₂+ +a₁₁ 12 = a₀+a₁₁ 2 & = a₁+a₁₀ 2 = aligned ) Now, deviations from their mean are ( aligned & | x -a₀ |= |a₁₁-a₀ | 2 = 11|d| 2 & | x -a₁ |= |a₁₀-a₁ | 2 = 9|d| 2 , . . . and so on aligned ) So, sum of deviations ( aligned & =2 [ 11|d| 2 + 9|d| 2 + 7|d| 2 + 5|d| 2 + 3|d| 2 + |d| 2 ] & =36|d| aligned ) ( ) Mean deviation from their arithmetic mean is ( 36|d| 12 =3|d| ) Hence, option (3) is correct.

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