Measures of Central Tendency and DispersionMCQMTP March 21Question 3110 of 473
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Find the mean deviation about mean for the numbers: $2, 6, 7, 4, 8, 3$

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — 2\displaystyle 2

All Options:

  • A1\displaystyle 1
  • B2\displaystyle 2
  • C5\displaystyle 5
  • D6\displaystyle 6

Detailed Solution & Explanation

We are given the observations: $2, 6, 7, 4, 8, 3$. The number of observations is $n = 6$. 1. Calculate the arithmetic mean (xˉ\displaystyle xˉ\displaystyle \bar{x}): xˉ=2+6+7+4+8+36=306=5xˉ=2+6+7+4+8+36=306=5\displaystyle \bar{x} = \frac{2 + 6 + 7 + 4 + 8 + 3}{6} = \frac{30}{6} = 5 2. Calculate absolute deviations from the mean ∣xi−5∣\displaystyle |x_i - 5|: - ∣2−5∣=3\displaystyle |2 - 5| = 3 - ∣6−5∣=1\displaystyle |6 - 5| = 1 - ∣7−5∣=2\displaystyle |7 - 5| = 2 - ∣4−5∣=1\displaystyle |4 - 5| = 1 - ∣8−5∣=3\displaystyle |8 - 5| = 3 - ∣3−5∣=2\displaystyle |3 - 5| = 2 3. Calculate sum of absolute deviations: ∑∣xi−5∣=3+1+2+1+3+2=12∑\displaystyle \sum |x_i - 5| = 3 + 1 + 2 + 1 + 3 + 2 = 12 4. Calculate Mean Deviation about Mean: M.D.=126=2M.D.=126=2\displaystyle \text{M.D.} = \frac{12}{6} = 2 Hence, **Option B** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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