Statistical Description of DataPYQ June 24Question 2709 of 295
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A perpendicular drawn from the point of intersection of two Ogive on the horizontal axis given the value of

Options

A2nd\displaystyle 2^{nd} Quartile
B3rd\displaystyle 3^{rd} Quartile
CMode
D1st\displaystyle 1^{st} Quartile
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Correct Answer

✅ Option a — 2nd\displaystyle 2^{nd} Quartile

All Options:

  • A2nd\displaystyle 2^{nd} Quartile
  • B3rd\displaystyle 3^{rd} Quartile
  • CMode
  • D1st\displaystyle 1^{st} Quartile

Detailed Solution & Explanation

The "less than" and "more than" ogives of a frequency distribution intersect at a specific point. Because the "less than" ogive starts at cumulative frequency 0\displaystyle 0 and goes to N\displaystyle N (total frequency) and the "more than" ogive starts at N\displaystyle N and goes to 0\displaystyle 0, their intersection point on the vertical axis corresponds to a cumulative frequency value of exactly N/2\displaystyle N/2. By definition, the value on the horizontal axis corresponding to a cumulative frequency of N/2\displaystyle N/2 is the **Median** of the distribution. In terms of quartiles: - The first quartile (Q1\displaystyle Q_1) corresponds to N/4\displaystyle N/4. - The second quartile (Q2\displaystyle Q_2) corresponds to 2N/4=N/2\displaystyle 2N/4 = N/2, which is identical to the Median. - The third quartile (Q3\displaystyle Q_3) corresponds to 3N/4\displaystyle 3N/4. Since the intersection point represents the median (N/2\displaystyle N/2), dropping a perpendicular from this point to the horizontal axis gives the value of the median, which is the **2nd Quartile** (Q2\displaystyle Q_2). Hence, **Option A** is the correct answer.

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