Central Tendency & DispersionPYQ 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.

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.

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