Central Tendency & DispersionPYQ June 22Question 3097 of 473
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Mean Deviation of data 3,10,10,4,7,18,5\displaystyle 3, 10, 10, 4, 7, 18, 5 from mode is

Options

A4.39
B4.70
C4.14
D5.24
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Correct Answer

✅ Option c — 4.14

All Options:

  • A4.39
  • B4.70
  • C4.14
  • D5.24

Detailed Solution & Explanation

We are given the dataset: 3,10,10,4,7,18,5\displaystyle 3, 10, 10, 4, 7, 18, 5. The number of observations is n=7\displaystyle n = 7. 1. Identify the Mode: The mode is the observation with the highest frequency. Here, 10\displaystyle 10 appears twice while all other observations appear once. Thus, Mode=10\displaystyle \text{Mode} = 10. 2. Calculate absolute deviations from the mode ∣xi−Mode∣\displaystyle |x_i - \text{Mode}|: - ∣3−10∣=7\displaystyle |3 - 10| = 7 - ∣10−10∣=0\displaystyle |10 - 10| = 0 - ∣10−10∣=0\displaystyle |10 - 10| = 0 - ∣4−10∣=6\displaystyle |4 - 10| = 6 - ∣7−10∣=3\displaystyle |7 - 10| = 3 - ∣18−10∣=8\displaystyle |18 - 10| = 8 - ∣5−10∣=5\displaystyle |5 - 10| = 5 3. Calculate sum of absolute deviations: ∑∣xi−Mode∣=7+0+0+6+3+8+5=29\sum |x_i - \text{Mode}| = 7 + 0 + 0 + 6 + 3 + 8 + 5 = 29 4. Calculate Mean Deviation about Mode: M.D.=297≈4.14\text{M.D.} = \frac{29}{7} \approx 4.14 Hence, **Option C** is the correct answer.

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