Measures of Central Tendency and DispersionMCQPYQ Jun 23Question 3004 of 473
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Find the mode of the following data:X | F(x)25-30 | 2030-35 | 5335-40 | 4240-45 | 4245-50 | 4150-55 | 43

Options

A31.75\displaystyle 31.75
B30.75\displaystyle 30.75
C33.75\displaystyle 33.75
D35.75\displaystyle 35.75
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Correct Answer

✅ Option c — 33.75\displaystyle 33.75

All Options:

  • A31.75\displaystyle 31.75
  • B30.75\displaystyle 30.75
  • C33.75\displaystyle 33.75
  • D35.75\displaystyle 35.75

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Detailed Solution & Explanation

**Step 1: Identify the modal class.** Frequencies: 25-30: 20, 30-35: 53, 35-40: 42, 40-45: 42, 45-50: 41, 50-55: 43. Highest frequency = 53, so modal class is **30-35**. **Step 2: Identify values for the mode formula.** - L=30\displaystyle L = 30 - f1=53\displaystyle f_1 = 53 - f0=20\displaystyle f_0 = 20 (pre-modal class frequency) - f2=42\displaystyle f_2 = 42 (post-modal class frequency) - h=5\displaystyle h = 5 **Step 3: Apply the formula.** Mode=L+f1−f02f1−f0−f2×h\text{Mode} = L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h =30+53−202(53)−20−42×5= 30 + \frac{53 - 20}{2(53) - 20 - 42} \times 5 =30+33106−62×5= 30 + \frac{33}{106 - 62} \times 5 =30+3344×5= 30 + \frac{33}{44} \times 5 =30+16544=30+3.75=33.75= 30 + \frac{165}{44} = 30 + 3.75 = 33.75 This matches **Option C** (33.75\displaystyle 33.75), not Option B. The computed answer is 33.75\displaystyle 33.75. Hence, **Option C** 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.

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