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Calculate the mean deviation about the mean of the set of first ten even natural numbers.

Options

  1. A5.5
  2. B2.5
  3. C5
  4. D0

Correct answer

C. 5

Step-by-step solution

The first ten even natural numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 . The mean x is given by x = 1 10 _ i=1 ¹⁰ x_i = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 10 = 110 10 = 11 . The mean deviation about the mean is calculated as MD ( x ) = 1 n _ i=1 ^ n |x_i - x | . Calculating the absolute deviations |x_i - 11| : |2-11| = 9 |4-11| = 7 |6-11| = 5 |8-11| = 3 |10-11| = 1 |12-11| = 1 |14-11| = 3 |16-11| = 5 |18-11| = 7 |20-11| = 9 Sum of absolute deviations = 9 + 7 + 5 + 3 + 1 + 1 + 3 + 5 + 7 + 9 = 50 . Mean d

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