Question:
What is the Median of the frequency distribution?
Statement (I): The Arithmetic Mean of the frequency distribution is 25.
Statement (II): The Mode of the frequency distribution is 28.
What is the Median of the frequency distribution?
Statement (I): The Arithmetic Mean of the frequency distribution is 25.
Statement (II): The Mode of the frequency distribution is 28.
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Do not assume the empirical relation among mean, median and mode is exact unless specifically stated.
Updated On: Jun 12, 2026
- Statement I alone is sufficient, but Statement II alone is not sufficient.
- Statement II alone is sufficient, but Statement I alone is not sufficient.
- Both statements together are sufficient, but neither statement alone is sufficient.
- Even both statements together are not sufficient.
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The Correct Option is D
Solution and Explanation
Concept:
Mean, median and mode are different measures of central tendency.
Knowing one or two of them generally does not determine the third exactly.
Step 1: Analyze Statement (I). Mean = 25. Many distributions can have mean 25 but different medians. Statement (I) is insufficient.
Step 2: Analyze Statement (II). Mode = 28. Many distributions can have mode 28 but different medians. Statement (II) is insufficient.
Step 3: Combine both statements. Even knowing \[ \text{Mean}=25 \] and \[ \text{Mode}=28, \] the median is not uniquely determined. The empirical relation \[ \text{Mode}=3(\text{Median})-2(\text{Mean}) \] is only an approximation and cannot be used to uniquely determine the median in general. Hence information remains insufficient.
Step 1: Analyze Statement (I). Mean = 25. Many distributions can have mean 25 but different medians. Statement (I) is insufficient.
Step 2: Analyze Statement (II). Mode = 28. Many distributions can have mode 28 but different medians. Statement (II) is insufficient.
Step 3: Combine both statements. Even knowing \[ \text{Mean}=25 \] and \[ \text{Mode}=28, \] the median is not uniquely determined. The empirical relation \[ \text{Mode}=3(\text{Median})-2(\text{Mean}) \] is only an approximation and cannot be used to uniquely determine the median in general. Hence information remains insufficient.
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