Central Tendency & DispersionPYQ June 23Question 3100 of 473
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The mean deviation about the mean for the data 12,16,24,30,35,39,40\displaystyle 12, 16, 24, 30, 35, 39, 40 is

Options

A9.14
B9.41
C8.91
D9.81
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Correct Answer

✅ Option a — 9.14

All Options:

  • A9.14
  • B9.41
  • C8.91
  • D9.81

Detailed Solution & Explanation

We are given the observations: 12,16,24,30,35,39,40\displaystyle 12, 16, 24, 30, 35, 39, 40. The number of observations is n=7\displaystyle n = 7. 1. Find the arithmetic mean (xˉ\displaystyle \bar{x}): xˉ=12+16+24+30+35+39+407=1967=28\bar{x} = \frac{12 + 16 + 24 + 30 + 35 + 39 + 40}{7} = \frac{196}{7} = 28 2. Find the absolute deviations from the mean ∣xi−xˉ∣\displaystyle |x_i - \bar{x}|: - ∣12−28∣=16\displaystyle |12 - 28| = 16 - ∣16−28∣=12\displaystyle |16 - 28| = 12 - ∣24−28∣=4\displaystyle |24 - 28| = 4 - ∣30−28∣=2\displaystyle |30 - 28| = 2 - ∣35−28∣=7\displaystyle |35 - 28| = 7 - ∣39−28∣=11\displaystyle |39 - 28| = 11 - ∣40−28∣=12\displaystyle |40 - 28| = 12 3. Calculate the sum of absolute deviations: ∑∣xi−xˉ∣=16+12+4+2+7+11+12=64\sum |x_i - \bar{x}| = 16 + 12 + 4 + 2 + 7 + 11 + 12 = 64 4. Calculate Mean Deviation about Mean: M.D.=647≈9.14\text{M.D.} = \frac{64}{7} \approx 9.14 Hence, **Option A** is the correct answer.

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