Central Tendency & DispersionPYQ Jan 21Question 3092 of 473
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Find the coefficient of mean deviation for mean for the data: 5,7,8,10,11,13,19\displaystyle 5, 7, 8, 10, 11, 13, 19

Options

A17.28
B28.57
C32.11
D18.56
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Correct Answer

✅ Option c — 32.11

All Options:

  • A17.28
  • B28.57
  • C32.11
  • D18.56

Detailed Solution & Explanation

We are given the observations: 5,7,8,10,11,13,19\displaystyle 5, 7, 8, 10, 11, 13, 19. The number of observations is n=7\displaystyle n = 7. 1. Calculate the arithmetic mean (xˉ\displaystyle \bar{x}): xˉ=5+7+8+10+11+13+197=737≈10.43\bar{x} = \frac{5 + 7 + 8 + 10 + 11 + 13 + 19}{7} = \frac{73}{7} \approx 10.43 2. Calculate absolute deviations from the mean ∣xi−xˉ∣\displaystyle |x_i - \bar{x}|: - ∣5−10.43∣=5.43\displaystyle |5 - 10.43| = 5.43 - ∣7−10.43∣=3.43\displaystyle |7 - 10.43| = 3.43 - ∣8−10.43∣=2.43\displaystyle |8 - 10.43| = 2.43 - ∣10−10.43∣=0.43\displaystyle |10 - 10.43| = 0.43 - ∣11−10.43∣=0.57\displaystyle |11 - 10.43| = 0.57 - ∣13−10.43∣=2.57\displaystyle |13 - 10.43| = 2.57 - ∣19−10.43∣=8.57\displaystyle |19 - 10.43| = 8.57 3. Calculate sum of absolute deviations: ∑∣xi−xˉ∣=5.43+3.43+2.43+0.43+0.57+2.57+8.57=23.43\sum |x_i - \bar{x}| = 5.43 + 3.43 + 2.43 + 0.43 + 0.57 + 2.57 + 8.57 = 23.43 4. Calculate Mean Deviation (M.D.): M.D.=∑∣xi−xˉ∣n=23.437≈3.35\text{M.D.} = \frac{\sum |x_i - \bar{x}|}{n} = \frac{23.43}{7} \approx 3.35 5. Calculate Coefficient of Mean Deviation about Mean: Coefficient=M.D.xˉ×100=3.3510.43×100≈32.11%\text{Coefficient} = \frac{\text{M.D.}}{\bar{x}} \times 100 = \frac{3.35}{10.43} \times 100 \approx 32.11\% Hence, **Option C** is the correct answer.

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