Measures of Central Tendency and DispersionMCQMTP Mar 21, MTP Apr 21Question 3087 of 473
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What is the coefficient of range for below: Class | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 Freq. | 11 | 25 | 16 | 7 | 3

Options

A22
B50
C75.82
D72.46
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Correct Answer

✅ Option d — 72.46

All Options:

  • A22
  • B50
  • C75.82
  • D72.46

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Detailed Solution & Explanation

We are given the grouped frequency distribution with class intervals: 10−19,20−29,30−39,40−49,50−59\displaystyle 10-19, 20-29, 30-39, 40-49, 50-59. 1. Find the class boundaries of the first and last class intervals: - First class boundary: 9.5−19.5  ⟹  Lower boundary of first class (L1)=9.5\displaystyle 9.5 - 19.5 \implies \text{Lower boundary of first class } (L_1) = 9.5 - Last class boundary: 49.5−59.5  ⟹  Upper boundary of last class (Un)=59.5\displaystyle 49.5 - 59.5 \implies \text{Upper boundary of last class } (U_n) = 59.5 2. Calculate the Range: Range=Un−L1=59.5−9.5=50\text{Range} = U_n - L_1 = 59.5 - 9.5 = 50 3. Calculate the Sum of boundaries: Sum=Un+L1=59.5+9.5=69\text{Sum} = U_n + L_1 = 59.5 + 9.5 = 69 4. Calculate the Coefficient of Range: Coefficient of Range=Un−L1Un+L1×100=5069×100≈72.46%\text{Coefficient of Range} = \frac{U_n - L_1}{U_n + L_1} \times 100 = \frac{50}{69} \times 100 \approx 72.46\% 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.

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