Statistical Description of DataMTP March 22Question 2739 of 295
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For the non-overlapping classes 0−19\displaystyle 0-19, 20−39\displaystyle 20-39, 40−59\displaystyle 40-59 the class mark of the class 0−19\displaystyle 0-19 is

Options

A0\displaystyle 0
B19\displaystyle 19
C9.5\displaystyle 9.5
DNone of these
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Correct Answer

✅ Option c — 9.5\displaystyle 9.5

All Options:

  • A0\displaystyle 0
  • B19\displaystyle 19
  • C9.5\displaystyle 9.5
  • DNone of these

Detailed Solution & Explanation

For any class interval in a frequency distribution, the **class mark** (also known as the mid-point or mid-value) is calculated as the arithmetic average of the lower and upper limits of that class: Class Mark=Lower Class Limit+Upper Class Limit2\text{Class Mark} = \frac{\text{Lower Class Limit} + \text{Upper Class Limit}}{2} For the first class interval, 0−19\displaystyle 0-19: - The Lower Class Limit is 0\displaystyle 0. - The Upper Class Limit is 19\displaystyle 19. Applying the formula: Class Mark=0+192=192=9.5\text{Class Mark} = \frac{0 + 19}{2} = \frac{19}{2} = 9.5 Even if we convert the inclusive classes to exclusive class boundaries (which would be −0.5\displaystyle -0.5 to 19.5\displaystyle 19.5), the class mark remains the same: Class Mark=−0.5+19.52=192=9.5\text{Class Mark} = \frac{-0.5 + 19.5}{2} = \frac{19}{2} = 9.5 This matches Option C. Hence, **Option C** is the correct answer.

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