Correct option is A
Given:
Mode - Mean = 10.8
Formula Used:
Empirical relationship between Mean, Median, and Mode:
Mode = 3 × Median - 2 × Mean
Solution:
From the given condition, we can express Mode in terms of Mean.
Mode = Mean + 10.8
We substitute this expression for Mode into the empirical formula.
Mean + 10.8 = 3 × Median - 2 × Mean
Rearranging the terms, we bring Mean to one side.
3 × Mean + 10.8 = 3 × Median
Dividing the entire equation by 3 gives:
Mean + 3.6 = Median
This implies that Median = Mean + 3.6.
We need to find the value by which the mode exceeds the median (Mode - Median).
Mode - Median = (Mean + 10.8) - (Mean + 3.6)
Mode - Median = 10.8 - 3.6 = 7.2
Final Answer
So the correct answer is (a)
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