Central Tendency & DispersionMTP June 2023 Series IIQuestion 2917 of 473
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The average of 'r\displaystyle r' consecutive numbers starting from 1\displaystyle 1 is 'r\displaystyle r'. If 2\displaystyle 2 is added to each of the number. Then the new average will be?

Options

Ar+s\displaystyle r+s
Br+(s/2)\displaystyle r+(s/2)
Cr\displaystyle r
DNone of these
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Correct Answer

✅ Option a — r+s\displaystyle r+s

All Options:

  • Ar+s\displaystyle r+s
  • Br+(s/2)\displaystyle r+(s/2)
  • Cr\displaystyle r
  • DNone of these

Detailed Solution & Explanation

**Step 1: Clarify the question.** The question says the average of r\displaystyle r consecutive numbers starting from 1 is r\displaystyle r. The average of first r\displaystyle r natural numbers (1, 2, ..., r\displaystyle r) is: xˉ=r+12\bar{x} = \frac{r+1}{2} For this to equal r\displaystyle r: r+12=r⇒r+1=2r⇒r=1\displaystyle \frac{r+1}{2} = r \Rightarrow r+1 = 2r \Rightarrow r = 1. This only works for r=1\displaystyle r=1. The question may be using a different statement — that the current average is some value. **Step 2: Effect of adding 2 to each number.** If each number has 2 added to it, the new average =\displaystyle = old average +2\displaystyle + 2. If old average =r\displaystyle = r, new average =r+2\displaystyle = r + 2. This is "None of these" if options don't include r+2\displaystyle r+2, or Option A if s=2\displaystyle s = 2 (which seems to be the case based on context — s\displaystyle s likely represents the constant added, which is 2). With s=2\displaystyle s=2, Option A gives r+s=r+2\displaystyle r + s = r + 2 which is correct. Hence, **Option A** is the correct answer.

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