Measures of Central Tendency and DispersionMCQPYQ Nov. 19Question 2990 of 473
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Find the mode of the following data:Class | 3-6 | 6-9 | 9-12 | 12-15 | 15-18 | 18-21Freq. | 2 | 5 | 10 | 23 | 21 | 12

Options

A25\displaystyle 25
B4.6\displaystyle 4.6
C14.6\displaystyle 14.6
D13.5\displaystyle 13.5
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Correct Answer

✅ Option c — 14.6\displaystyle 14.6

All Options:

  • A25\displaystyle 25
  • B4.6\displaystyle 4.6
  • C14.6\displaystyle 14.6
  • D13.5\displaystyle 13.5

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Detailed Solution & Explanation

**Step 1: Identify the modal class.** Frequencies: 3-6: 2, 6-9: 5, 9-12: 10, 12-15: 23, 15-18: 21, 18-21: 12. The highest frequency is 23, so the modal class is **12-15**. **Step 2: Identify values for the mode formula.** - L\displaystyle L = lower boundary of modal class = 12\displaystyle 12 - f1\displaystyle f_1 = frequency of modal class = 23\displaystyle 23 - f0\displaystyle f_0 = frequency of pre-modal class = 10\displaystyle 10 - f2\displaystyle f_2 = frequency of post-modal class = 21\displaystyle 21 - h\displaystyle h = class width = 3\displaystyle 3 **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 =12+23−102(23)−10−21×3= 12 + \frac{23 - 10}{2(23) - 10 - 21} \times 3 =12+1346−31×3= 12 + \frac{13}{46 - 31} \times 3 =12+1315×3= 12 + \frac{13}{15} \times 3 =12+3915=12+2.6=14.6= 12 + \frac{39}{15} = 12 + 2.6 = 14.6 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.

Related Comparison Tables

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