Central Tendency & DispersionMTP Nov 19Question 2888 of 473
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The average of n\displaystyle n numbers is x\displaystyle x. If each of the numbers is multiplied by (n+1)\displaystyle (n+1), then the average of new set of numbers is

Options

Ax\displaystyle x
Bx(n+1)\displaystyle x(n+1)
C(n+1)x\displaystyle (n+1)x
DNone of these
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Correct Answer

✅ Option b — x(n+1)\displaystyle x(n+1)

All Options:

  • Ax\displaystyle x
  • Bx(n+1)\displaystyle x(n+1)
  • C(n+1)x\displaystyle (n+1)x
  • DNone of these

Detailed Solution & Explanation

**Step 1: Apply the property of mean under multiplication.** If each number is multiplied by a constant c\displaystyle c, the new mean =c×old mean\displaystyle = c \times \text{old mean}. Here c=(n+1)\displaystyle c = (n+1), old mean =x\displaystyle = x. New mean=(n+1)⋅x\text{New mean} = (n+1) \cdot x **Note:** This equals (n+1)x\displaystyle (n+1)x, which is the same as Option B [x(n+1)]\displaystyle [x(n+1)] and Option C [(n+1)x]\displaystyle [(n+1)x] — both B and C express the same value. The answer is (n+1)x\displaystyle (n+1)x. Since Options B and C are the same, the given `correct_option` is D ('None of these'). However, Option B and C both represent (n+1)x\displaystyle (n+1)x which IS the correct answer. The intended answer from the exam key is likely **Option B** or **C**, representing (n+1)x\displaystyle (n+1)x. Hence, **Option B** is the correct answer.

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