Central Tendency & DispersionPYQ July 21Question 3096 of 473
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The mean deviation of the numbers 3,10,6,11,14,17,9,8,12\displaystyle 3, 10, 6, 11, 14, 17, 9, 8, 12 about the mean is:

Options

A8.7
B4.2
C3.1
D9.8
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Correct Answer

✅ Option c — 3.1

All Options:

  • A8.7
  • B4.2
  • C3.1
  • D9.8

Detailed Solution & Explanation

We are given the dataset: 3,10,6,11,14,17,9,8,12\displaystyle 3, 10, 6, 11, 14, 17, 9, 8, 12. The number of observations is n=9\displaystyle n = 9. 1. Calculate the arithmetic mean (xˉ\displaystyle \bar{x}): xˉ=3+10+6+11+14+17+9+8+129=909=10\bar{x} = \frac{3 + 10 + 6 + 11 + 14 + 17 + 9 + 8 + 12}{9} = \frac{90}{9} = 10 2. Calculate absolute deviations from the mean ∣xi−xˉ∣\displaystyle |x_i - \bar{x}|: - ∣3−10∣=7\displaystyle |3 - 10| = 7 - ∣10−10∣=0\displaystyle |10 - 10| = 0 - ∣6−10∣=4\displaystyle |6 - 10| = 4 - ∣11−10∣=1\displaystyle |11 - 10| = 1 - ∣14−10∣=4\displaystyle |14 - 10| = 4 - ∣17−10∣=7\displaystyle |17 - 10| = 7 - ∣9−10∣=1\displaystyle |9 - 10| = 1 - ∣8−10∣=2\displaystyle |8 - 10| = 2 - ∣12−10∣=2\displaystyle |12 - 10| = 2 3. Calculate the sum of absolute deviations: ∑∣xi−xˉ∣=7+0+4+1+4+7+1+2+2=28\sum |x_i - \bar{x}| = 7 + 0 + 4 + 1 + 4 + 7 + 1 + 2 + 2 = 28 4. Calculate Mean Deviation: M.D.=289≈3.11\text{M.D.} = \frac{28}{9} \approx 3.11 Hence, **Option C** is the correct answer.

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