Central Tendency & DispersionPYQ Jun 23Question 2874 of 473
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The mean of a set of 20 observations is 18.3. The mean is reduced by 0.6 when a new observation is added to the set. The new observation is:

Options

A17.6\displaystyle 17.6
B18.9\displaystyle 18.9
C5.7\displaystyle 5.7
D24.6\displaystyle 24.6
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Correct Answer

✅ Option c — 5.7\displaystyle 5.7

All Options:

  • A17.6\displaystyle 17.6
  • B18.9\displaystyle 18.9
  • C5.7\displaystyle 5.7
  • D24.6\displaystyle 24.6

Detailed Solution & Explanation

**Step 1: Compute the original total sum.** Sum of 20 observations=20×18.3=366\text{Sum of 20 observations} = 20 \times 18.3 = 366 **Step 2: Identify new mean and new total.** New mean =18.3−0.6=17.7\displaystyle = 18.3 - 0.6 = 17.7. Number of observations now =21\displaystyle = 21. New total sum=21×17.7=371.7\text{New total sum} = 21 \times 17.7 = 371.7 **Step 3: Find the new observation.** New observation=371.7−366=5.7\text{New observation} = 371.7 - 366 = 5.7 Hence, **Option C** is the correct answer.

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