Statistical Description of DataMTP June 2023 Series IIQuestion 2752 of 295
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Ogive for more than type and less than distributions intersect at

Options

AMean
BMedian
CMode
DOrigin
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Correct Answer

✅ Option b — Median

All Options:

  • AMean
  • BMedian
  • CMode
  • DOrigin

Detailed Solution & Explanation

The 'less than' ogive and the 'more than' ogive of a grouped frequency distribution are curves that plot cumulative frequencies from opposite directions: - The 'less than' ogive starts at cumulative frequency 0\displaystyle 0 and increases continuously to the total frequency N\displaystyle N. - The 'more than' ogive starts at the total frequency N\displaystyle N and decreases continuously to 0\displaystyle 0. Because of their monotonic and opposite directions, they must intersect at a unique point. At this intersection point, the cumulative frequency value represented on the vertical axis is exactly half of the total frequency, i.e., N/2\displaystyle N/2. By definition, the value on the horizontal x-axis corresponding to a cumulative frequency of N/2\displaystyle N/2 is the **Median** of the distribution. Thus, the x-coordinate of the intersection of these two curves is the Median. Hence, **Option B** is the correct answer.

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