Central Tendency & DispersionMTP Nov 20Question 3103 of 473
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The mean deviation about Mode for the numbers 4/11,6/11,8/11,9/11,12/11,8/11\displaystyle 4/11, 6/11, 8/11, 9/11, 12/11, 8/11 is

Options

A9/15\displaystyle 9/15
B12\displaystyle 12
C6/11\displaystyle 6/11
D1/6\displaystyle 1/6
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Correct Answer

✅ Option d — 1/6\displaystyle 1/6

All Options:

  • A9/15\displaystyle 9/15
  • B12\displaystyle 12
  • C6/11\displaystyle 6/11
  • D1/6\displaystyle 1/6

Detailed Solution & Explanation

We are given the observations: 4/11,6/11,8/11,9/11,12/11,8/11\displaystyle 4/11, 6/11, 8/11, 9/11, 12/11, 8/11. The number of observations is n=6\displaystyle n = 6. 1. Find the Mode: The mode is the observation with the highest frequency. Here, 8/11\displaystyle 8/11 appears twice while all other observations appear once. Thus, Mode=8/11\displaystyle \text{Mode} = 8/11. 2. Find absolute deviations from the mode ∣xi−Mode∣\displaystyle |x_i - \text{Mode}|: - ∣4/11−8/11∣=4/11\displaystyle |4/11 - 8/11| = 4/11 - ∣6/11−8/11∣=2/11\displaystyle |6/11 - 8/11| = 2/11 - ∣8/11−8/11∣=0\displaystyle |8/11 - 8/11| = 0 - ∣9/11−8/11∣=1/11\displaystyle |9/11 - 8/11| = 1/11 - ∣12/11−8/11∣=4/11\displaystyle |12/11 - 8/11| = 4/11 - ∣8/11−8/11∣=0\displaystyle |8/11 - 8/11| = 0 3. Calculate sum of absolute deviations: ∑∣xi−Mode∣=4+2+0+1+4+011=1111=1\sum |x_i - \text{Mode}| = \frac{4 + 2 + 0 + 1 + 4 + 0}{11} = \frac{11}{11} = 1 4. Calculate Mean Deviation about Mode: M.D.=16\text{M.D.} = \frac{1}{6} Hence, **Option D** is the correct answer.

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