Central Tendency & DispersionMTP June 24 Series IQuestion 2930 of 473
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When 10\displaystyle 10 is subtracted from all the observations, the mean is reduced to 60%\displaystyle 60\% of its value. If 5\displaystyle 5 is added to all the observations, then the mean will be

Options

A25
B30
C60
D65
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Correct Answer

✅ Option b — 30

All Options:

  • A25
  • B30
  • C60
  • D65

Detailed Solution & Explanation

**Step 1: Set up equation for first condition.** Let original mean =xˉ\displaystyle = \bar{x}. When 10 is subtracted from all observations: xˉ−10=0.6xˉ\bar{x} - 10 = 0.6\bar{x} 0.4xˉ=100.4\bar{x} = 10 xˉ=25\bar{x} = 25 **Step 2: Compute the new mean when 5 is added.** New mean=xˉ+5=25+5=30\text{New mean} = \bar{x} + 5 = 25 + 5 = 30 **Note:** The computed new mean is **30** (Option B), not 65 (Option D). Hence, **Option B** is the correct answer.

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