Central Tendency & DispersionMTP Dec 2023 Series IIQuestion 3204 of 473
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Mean and S.D. of a given set of observations is 1,500\displaystyle 1,500 and 400\displaystyle 400 respectively. If there is an increment of 100\displaystyle 100 in the first year and each observation is hiked by 20%\displaystyle 20\% in 2\displaystyle 2nd years, then find new mean and S.D.

Options

A1920,480\displaystyle 1920, 480
B1920,580\displaystyle 1920, 580
C1600,480\displaystyle 1600, 480
D1600,400\displaystyle 1600, 400
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Correct Answer

✅ Option a — 1920,480\displaystyle 1920, 480

All Options:

  • A1920,480\displaystyle 1920, 480
  • B1920,580\displaystyle 1920, 580
  • C1600,480\displaystyle 1600, 480
  • D1600,400\displaystyle 1600, 400

Detailed Solution & Explanation

**Given:** Original Mean = 1500, Original SD = 400 **Year 1: Increment of 100 (add 100 to each observation).** - New Mean = 1500+100=1600\displaystyle 1500 + 100 = 1600 - New SD = 400\displaystyle 400 (unchanged, since adding a constant doesn't affect SD) **Year 2: 20% hike (multiply each observation by 1.20).** - New Mean = 1600×1.20=1920\displaystyle 1600 \times 1.20 = 1920 - New SD = 400×1.20=480\displaystyle 400 \times 1.20 = 480 (SD scales proportionally) **Final: Mean = 1920, SD = 480** (Option A). The given `correct_option` 'd' (1600,400\displaystyle 1600, 400) represents only after Year 1, not after Year 2. After BOTH transformations: Mean = 1920, SD = 480. Hence, **Option A** is the correct answer.

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