Central Tendency & DispersionMTP 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

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.

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