Measures of Central Tendency and DispersionMCQPYQ July 21Question 3093 of 473
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If a school has $14$ teachers, their heights (in cm) are: $172, 173, 164, 178, 168, 169, 173, 172, 173, 164, 178, 168, 169, 173$ then average deviation of this data is:

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

✅ Option c — $3.43$ approx.

All Options:

  • A$2.43$ approx.
  • B$3.93$ approx.
  • C$3.43$ approx.
  • D$2.92$ approx.

Detailed Solution & Explanation

We are given $14$ observations of heights. The unique heights are $172, 173, 164, 178, 168, 169, 173$, each repeated twice. 1. Find the arithmetic mean (xˉ\displaystyle xˉ\displaystyle \bar{x}): xˉ=2(172+173+164+178+168+169+173)14=2(1197)14=171 cm\displaystyle \bar{x} = \frac{2(172 + 173 + 164 + 178 + 168 + 169 + 173)}{14} = 2(1197)14=171\displaystyle \frac{2(1197)}{14} = 171 cm\displaystyle \text{ cm} 2. Find the sum of absolute deviations from the mean: - ∣172−171∣×2=1×2=2\displaystyle |172 - 171| ×\displaystyle \times 2 = 1 ×\displaystyle \times 2 = 2 - ∣173−171∣×4=2×4=8\displaystyle |173 - 171| ×\displaystyle \times 4 = 2 ×\displaystyle \times 4 = 8 - ∣164−171∣×2=7×2=14\displaystyle |164 - 171| ×\displaystyle \times 2 = 7 ×\displaystyle \times 2 = 14 - ∣178−171∣×2=7×2=14\displaystyle |178 - 171| ×\displaystyle \times 2 = 7 ×\displaystyle \times 2 = 14 - ∣168−171∣×2=3×2=6\displaystyle |168 - 171| ×\displaystyle \times 2 = 3 ×\displaystyle \times 2 = 6 - ∣169−171∣×2=2×2=4\displaystyle |169 - 171| ×\displaystyle \times 2 = 2 ×\displaystyle \times 2 = 4 Total Sum=2+8+14+14+6+4=48Total Sum=2+8+14+14+6+4=48\displaystyle \text{Total Sum} = 2 + 8 + 14 + 14 + 6 + 4 = 48 3. Calculate Mean Deviation (average deviation): M.D.=4814≈3.43 cmM.D.=4814\displaystyle \text{M.D.} = \frac{48}{14} ≈\displaystyle \approx 3.43 cm\displaystyle \text{ cm} Hence, **Option C** 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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