Measures of Central Tendency and DispersionMCQMTP May 19Question 3011 of 473
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If x\displaystyle x and y\displaystyle y are related by x−y−10=0\displaystyle x - y - 10 = 0 and mode of x\displaystyle x is known to be 23\displaystyle 23, then the mode of y\displaystyle y is

Options

A20
B13
C3
D33
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Correct Answer

✅ Option b — 13

All Options:

  • A20
  • B13
  • C3
  • D33

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Detailed Solution & Explanation

**Step 1: Express y\displaystyle y in terms of x\displaystyle x.** From the relation x−y−10=0\displaystyle x - y - 10 = 0: y=x−10y = x - 10 **Step 2: Apply the mode transformation property.** If y=a+bx\displaystyle y = a + bx, then Mode(y)=a+b×\displaystyle (y) = a + b \times Mode(x)\displaystyle (x). Here y=x−10\displaystyle y = x - 10, so a=−10\displaystyle a = -10, b=1\displaystyle b = 1. **Step 3: Calculate mode of y\displaystyle y.** Mode(y)=−10+1×23=−10+23=13\text{Mode}(y) = -10 + 1 \times 23 = -10 + 23 = 13 This corresponds to **Option B** (13\displaystyle 13). Note: The given answer is C (3\displaystyle 3), but x−y−10=0⇒y=x−10=23−10=13\displaystyle x - y - 10 = 0 \Rightarrow y = x - 10 = 23 - 10 = 13. 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.

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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