If the mean of the numbers 0, (x+2), (3x+6), and (4x+8) is 4, find their mean deviation.

  • A 0
  • B 2
  • C 3
  • D 4

The correct answer is C. 3

Here is the solution in MathJax:

\(= \frac{0 + (x+2) + (3x+6) + (4x+8)}{4} \)

\(= \frac{8x + 16}{4} \)

\(= 2x + 4|)

Since the mean is equal to 4, we have 2x + 4 = 4, which implies that x = 0.

Substituting this value of x into the given numbers, we find that the numbers are 0, 2, 6, and 8. The mean of these numbers is (0 + 2 + 6 + 8) / 4 = 4.

The mean deviation of these numbers is the average of the absolute differences between each number and the mean, which is given by the formula:

Mean Deviation = \(\frac{|0 - 4| + |2 - 4| + |6 - 4| + |8 - 4|}{4} \)

\(= \frac{4 + 2 + 2 + 4}{4}= \frac{12}{4}= 3\)

Therefore, the mean deviation of the numbers is 3.

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