Central Tendency & DispersionICAI SM, MTP Apr 21Question 3177 of 473
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The of mean and SD of a series is a+b\displaystyle a+b, if we add 2 to each observation of the series then the sum of the mean and SD is

Options

Aa+b+2\displaystyle a+b+2
B6−a+b\displaystyle 6-a+b
C4+a−b\displaystyle 4+a-b
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
  • B6−a+b\displaystyle 6-a+b
  • C4+a−b\displaystyle 4+a-b
  • Da+b+4\displaystyle a+b+4

Detailed Solution & Explanation

**Given:** Mean + SD of original series = a+b\displaystyle a + b. Let Mean = xˉ\displaystyle \bar{x} and SD = σ\displaystyle \sigma, so xˉ+σ=a+b\displaystyle \bar{x} + \sigma = a + b. **When 2 is added to each observation:** - New Mean = xˉ+2\displaystyle \bar{x} + 2 (mean shifts by 2) - New SD = σ\displaystyle \sigma (SD is unaffected by adding a constant) **New sum of Mean and SD:** New Mean+New SD=(xˉ+2)+σ=(xˉ+σ)+2=(a+b)+2=a+b+2\text{New Mean} + \text{New SD} = (\bar{x} + 2) + \sigma = (\bar{x} + \sigma) + 2 = (a + b) + 2 = a + b + 2 Hence, **Option A** is the correct answer.

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