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

Options

A2.43\displaystyle 2.43 approx.
B3.93\displaystyle 3.93 approx.
C3.43\displaystyle 3.43 approx.
D2.92\displaystyle 2.92 approx.
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Correct Answer

✅ Option c — 3.43\displaystyle 3.43 approx.

All Options:

  • A2.43\displaystyle 2.43 approx.
  • B3.93\displaystyle 3.93 approx.
  • C3.43\displaystyle 3.43 approx.
  • D2.92\displaystyle 2.92 approx.

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Detailed Solution & Explanation

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