Central Tendency & DispersionMTP Apr 21Question 2897 of 473
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The sum of mean and SD of a series is a+b\displaystyle a+b, if we add 2 to each observations of the series then the sum of the mean and SD is

Options

Aa+b+2\displaystyle a+b+2
Ba+b\displaystyle a+b
C4+b+a\displaystyle 4+b+a
Da+b+4\displaystyle a+b+4
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Correct Answer

✅ Option a — a+b+2\displaystyle a+b+2

All Options:

  • Aa+b+2\displaystyle a+b+2
  • Ba+b\displaystyle a+b
  • C4+b+a\displaystyle 4+b+a
  • Da+b+4\displaystyle a+b+4

Detailed Solution & Explanation

**Step 1: Analyze the effect of adding a constant on mean and SD.** Let original mean =μ\displaystyle = \mu and original SD =σ\displaystyle = \sigma, so μ+σ=a+b\displaystyle \mu + \sigma = a + b (where a\displaystyle a represents the mean component and b\displaystyle b represents the SD). **Step 2: When 2 is added to each observation:** - New mean =μ+2\displaystyle = \mu + 2 - New SD =σ\displaystyle = \sigma (SD is unaffected by adding a constant) **Step 3: New sum of mean and SD.** New sum=(μ+2)+σ=(μ+σ)+2=(a+b)+2\text{New sum} = (\mu + 2) + \sigma = (\mu + \sigma) + 2 = (a + b) + 2 **Note:** This gives a+b+2\displaystyle a + b + 2 (Option A). The `correct_option` is C (4+b+a=a+b+4\displaystyle 4 + b + a = a + b + 4), which would mean 4 was added. However, we added 2, so the mean increases by 2, SD stays same, and the sum increases by 2. The correct answer is a+b+2\displaystyle a + b + 2. Hence, **Option A** is the correct answer.

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