Statistical Description of DataPYQ Sep 24Question 2717 of 295
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If the class intervals of certain data are 10−14,15−19,20−24\displaystyle 10-14, 15-19, 20-24, then the first class boundaries is

Options

A10−14\displaystyle 10-14
B9.5−14.5\displaystyle 9.5-14.5
C10−15\displaystyle 10-15
D10.5−15.5\displaystyle 10.5-15.5
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Correct Answer

✅ Option b — 9.5−14.5\displaystyle 9.5-14.5

All Options:

  • A10−14\displaystyle 10-14
  • B9.5−14.5\displaystyle 9.5-14.5
  • C10−15\displaystyle 10-15
  • D10.5−15.5\displaystyle 10.5-15.5

Detailed Solution & Explanation

The given class intervals are 10−14,15−19,20−24\displaystyle 10-14, 15-19, 20-24. This is an inclusive (or discontinuous) classification where both the lower limit and upper limit are included in the class, and there is a gap of 1\displaystyle 1 unit between the upper limit of one class (14\displaystyle 14) and the lower limit of the next class (15\displaystyle 15). To convert inclusive class limits into exclusive class boundaries, we must calculate a correction factor d\displaystyle d: d=Lower limit of next class−Upper limit of current class2=15−142=0.5d = \frac{\text{Lower limit of next class} - \text{Upper limit of current class}}{2} = \frac{15 - 14}{2} = 0.5 Now, we adjust the limits of the first class (10−14\displaystyle 10-14) to find the boundaries: - **Lower Class Boundary** = Lower Limit−d=10−0.5=9.5\displaystyle \text{Lower Limit} - d = 10 - 0.5 = 9.5 - **Upper Class Boundary** = Upper Limit+d=14+0.5=14.5\displaystyle \text{Upper Limit} + d = 14 + 0.5 = 14.5 Thus, the boundaries of the first class are 9.5−14.5\displaystyle 9.5-14.5. This matches Option B. Hence, **Option B** is the correct answer.

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