Measures of Central Tendency and DispersionMCQPYQ July 21Question 2995 of 473
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If y=3+1.9x\displaystyle y = 3 + 1.9x, and mode of x\displaystyle x is 15\displaystyle 15, then the mode of y\displaystyle y is:

Options

A15.9\displaystyle 15.9
B27.8\displaystyle 27.8
C35.7\displaystyle 35.7
D31.5\displaystyle 31.5
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Correct Answer

✅ Option d — 31.5\displaystyle 31.5

All Options:

  • A15.9\displaystyle 15.9
  • B27.8\displaystyle 27.8
  • C35.7\displaystyle 35.7
  • D31.5\displaystyle 31.5

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Detailed Solution & Explanation

**Step 1: Recall the property of mode under linear transformation.** If y=a+bx\displaystyle y = a + bx, then Mode(y)=a+b×\displaystyle (y) = a + b \times Mode(x)\displaystyle (x). **Step 2: Substitute given values.** - a=3\displaystyle a = 3, b=1.9\displaystyle b = 1.9, Mode(x)=15\displaystyle (x) = 15 **Step 3: Calculate.** Mode(y)=3+1.9×15=3+28.5=31.5\text{Mode}(y) = 3 + 1.9 \times 15 = 3 + 28.5 = 31.5 Wait, 3+1.9×15=3+28.5=31.5\displaystyle 3 + 1.9 \times 15 = 3 + 28.5 = 31.5 — this matches Option D. But the marked correct option is B (27.8\displaystyle 27.8). Let us check: 1.9×15=28.5\displaystyle 1.9 \times 15 = 28.5 and 3+28.5=31.5\displaystyle 3 + 28.5 = 31.5. This clearly gives 31.5\displaystyle 31.5. For Option B: 27.8=?\displaystyle 27.8 = ? → 1.9×13=24.7\displaystyle 1.9 \times 13 = 24.7, 3+24.7=27.7\displaystyle 3 + 24.7 = 27.7 not exactly. Or 1.9×14=26.6+3=29.6\displaystyle 1.9 \times 14 = 26.6 + 3 = 29.6. None match. The mathematically correct answer is 31.5\displaystyle 31.5 = **Option D**. Hence, **Option D** 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.

Key Concepts to Understand

Mode

The value that appears most frequently in a data set. A data set can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes). It is the only measure of central tendency applicable to qualitative (categorical) data.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central TendencyFiscal Policy vs Monetary Policy: CA Foundation Economics

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