Measures of Central Tendency and DispersionMCQPYQ Jan. 21Question 2994 of 473
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If y=3+(4.5)x\displaystyle y = 3 + (4.5)x and the mode for x\displaystyle x - value is $20$, then the mode for $y$ - value is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option d — $93$

All Options:

  • A$3.225$
  • B$12$
  • C$24.5$
  • D$93$

Detailed Solution & Explanation

**Step 1: Recall the property of mode under linear transformation.** If y=a+bx\displaystyle y = a + bx, then Mode(y)\displaystyle (y) = a+b×\displaystyle a + b ×\displaystyle \times Mode(x)\displaystyle (x). **Step 2: Given information.** - y=3+4.5x\displaystyle y = 3 + 4.5x - Mode of x=20\displaystyle x = 20 **Step 3: Calculate mode of y\displaystyle y.** Mode(y)=3+4.5×20=3+90=93Mode\displaystyle \text{Mode}(y) = 3 + 4.5 ×\displaystyle \times 20 = 3 + 90 = 93 So Mode(y\displaystyle y) = $93$, which corresponds to **Option D**. However, the given correct answer is B ($12).Letusre−examine:perhapsthequestionmeans\displaystyle ). Let us re-examine: perhaps the question meansy = 3 + 4.5x$ but the actual relationship should be read differently, or perhaps it's $y = (3 + 4.5)x = 7.5x×\displaystyle \times …" style="color:#cc0000">\displaystyle which gives $7.5 ×\displaystyle \times 20 = 150 — that doesn't match either. Alternatively, maybe the relationship is y=34.5+x\displaystyle y = 34.5+x\displaystyle \frac{3}{4.5} + x or something else. Given the options, let's check option D: 3+4.5×20=93\displaystyle 3 + 4.5 ×\displaystyle \times 20 = 93 ✓ (Option D). Computing directly: Mode(y)=3+4.5×20=93\displaystyle (y) = 3 + 4.5 ×\displaystyle \times 20 = 93. 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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