Measures of Central Tendency and DispersionMCQICAI SM, MTP Nov 20Question 2890 of 473
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Two variables assume the values 1,2,…,5\displaystyle 1, 2, \dots, 5 with frequencies as 1,2,3,…,5\displaystyle 1, 2, 3, \dots, 5 then what is the AM?

Options

A113\displaystyle \frac{11}{3}
B158\displaystyle \frac{15}{8}
C4.86
D10
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Correct Answer

✅ Option a — 113\displaystyle \frac{11}{3}

All Options:

  • A113\displaystyle \frac{11}{3}
  • B158\displaystyle \frac{15}{8}
  • C4.86
  • D10

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Detailed Solution & Explanation

**Step 1: Set up the frequency table.** | Value (x\displaystyle x) | Frequency (f\displaystyle f) | fx\displaystyle fx | |-------------|-----------------|------| | 1 | 1 | 1 | | 2 | 2 | 4 | | 3 | 3 | 9 | | 4 | 4 | 16 | | 5 | 5 | 25 | **Step 2: Compute totals.** ∑f=1+2+3+4+5=15\sum f = 1+2+3+4+5 = 15 ∑fx=1+4+9+16+25=55\sum fx = 1+4+9+16+25 = 55 **Step 3: Compute AM.** xˉ=∑fx∑f=5515=113\bar{x} = \frac{\sum fx}{\sum f} = \frac{55}{15} = \frac{11}{3} 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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