Measures of Central Tendency and DispersionMCQPYQ July 21Question 2864 of 473
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The mean of 'n\displaystyle n' observation is 'x\displaystyle x'. If k\displaystyle k is added to each observation, then the new mean is.

Options

Ak\displaystyle k
Bx+k\displaystyle x+k
Cx−k\displaystyle x-k
Dx\displaystyle x
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Correct Answer

✅ Option b — x+k\displaystyle x+k

All Options:

  • Ak\displaystyle k
  • Bx+k\displaystyle x+k
  • Cx−k\displaystyle x-k
  • Dx\displaystyle x

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Detailed Solution & Explanation

**Step 1: Apply the property of arithmetic mean.** Let the observations be x1,x2,…,xn\displaystyle x_1, x_2, \ldots, x_n with mean x\displaystyle x (denoting xˉ\displaystyle \bar{x}). New observations: xi′=xi+k\displaystyle x_i' = x_i + k. **Step 2: Compute the new mean.** xˉ′=∑(xi+k)n=∑xi+nkn=∑xin+k=x+k\bar{x}' = \frac{\sum(x_i + k)}{n} = \frac{\sum x_i + nk}{n} = \frac{\sum x_i}{n} + k = x + k **Note:** The mathematically correct answer is x+k\displaystyle x + k (Option B). The `correct_option` field says D (x\displaystyle x), which is incorrect — adding k\displaystyle k to each observation increases the mean by k\displaystyle k. The logically correct answer is **x+k\displaystyle x + k**. Hence, **Option B** 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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