Central Tendency & DispersionPYQ Dec 22Question 2870 of 473
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The mean of 50 observations is 36. If two observations 30 and 42 are to be excluded, then the mean of the remaining observations will be:

Options

A36\displaystyle 36
B38\displaystyle 38
C48\displaystyle 48
D50\displaystyle 50
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Correct Answer

✅ Option a — 36\displaystyle 36

All Options:

  • A36\displaystyle 36
  • B38\displaystyle 38
  • C48\displaystyle 48
  • D50\displaystyle 50

Detailed Solution & Explanation

**Step 1: Compute the original total sum.** Total sum=50×36=1800\text{Total sum} = 50 \times 36 = 1800 **Step 2: Compute the sum after exclusion.** Excluded observations: 30 and 42. Their sum =30+42=72\displaystyle = 30 + 42 = 72. Remaining sum=1800−72=1728\text{Remaining sum} = 1800 - 72 = 1728 **Step 3: Number of remaining observations.** nremaining=50−2=48n_{remaining} = 50 - 2 = 48 **Step 4: New mean.** xˉnew=172848=36\bar{x}_{new} = \frac{1728}{48} = 36 The mean remains **36**. Hence, **Option A** is the correct answer.

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