Central Tendency & DispersionPYQ June 19Question 3122 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\displaystyle 2 to each observation of the series then the sum of mean and SD is

Options

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

Detailed Solution & Explanation

We are given: - Sum of mean and standard deviation: xˉ+σ=a+b\displaystyle \bar{x} + \sigma = a + b, where xˉ=a\displaystyle \bar{x} = a and σ=b\displaystyle \sigma = b. If we add 2\displaystyle 2 to each observation of the series: 1. The new mean is: xˉnew=xˉ+2=a+2\displaystyle \bar{x}_{\text{new}} = \bar{x} + 2 = a + 2 2. The standard deviation is independent of change of origin, so the new standard deviation remains: σnew=σ=b\displaystyle \sigma_{\text{new}} = \sigma = b 3. Calculate the new sum of the mean and standard deviation: New Sum=xˉnew+σnew=(a+2)+b=a+b+2\text{New Sum} = \bar{x}_{\text{new}} + \sigma_{\text{new}} = (a + 2) + b = a + b + 2 Hence, **Option A** is the correct answer.

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