Central Tendency & DispersionPYQ June 22Question 2869 of 473
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The mean of 20 observation is 38. If two observation are taken as 84 and 36 instead of 48 and 63 find new means.

Options

A38.45\displaystyle 38.45
B41.15\displaystyle 41.15
C37.55\displaystyle 37.55
D40.05\displaystyle 40.05
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Correct Answer

✅ Option c — 37.55\displaystyle 37.55

All Options:

  • A38.45\displaystyle 38.45
  • B41.15\displaystyle 41.15
  • C37.55\displaystyle 37.55
  • D40.05\displaystyle 40.05

Detailed Solution & Explanation

**Step 1: Find the original total sum.** Original sum=20×38=760\text{Original sum} = 20 \times 38 = 760 **Step 2: Identify the error.** Wrong values used: 84 and 36 (instead of correct values 48 and 63). **Step 3: Compute the corrected sum.** Corrected sum=Original sum−Wrong values+Correct values\text{Corrected sum} = \text{Original sum} - \text{Wrong values} + \text{Correct values} =760−(84+36)+(48+63)= 760 - (84 + 36) + (48 + 63) =760−120+111= 760 - 120 + 111 =751= 751 **Step 4: Compute the new mean.** New mean=75120=37.55\text{New mean} = \frac{751}{20} = 37.55 Hence, **Option C** is the correct answer.

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