Find the median using an empirical relation, when it is given that mode and mean are 8 and 9 respectively.
Answers
The relation between Mean, Median and Mode of the given data is:
Mode = 3Median − 2Mean
⟹ 8 = 3Median − 2 × 9
⟹ 3Median = 8 + 18
⟹ Median = 26/3
⟹ Median = 8.67
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Find the median using an empirical relation, when it is given that mode and mean are 8 and 9 respectively.
Explanation:
Empirical median mode relationship is given as: Mean – Mode = 3 (Mean – Median)
Given:
Mode = 8, Mean = 9.
substituting the values in the given relationship above,
9 - 8 = 3(9 - Median)
Let Median = x
9 - 8 = 3(9 - x)
1 = 27 - 3x
1 + 3x = 27
3x = 27 - 1
x = 26 ÷ 3
x = 8.66
Therefore, Median = 8.66.
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