Measures of Central Tendency and DispersionMCQPYQ 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

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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.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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