If the ratio of the mode and the median of a distribution is 6 : 5, then the…
2019
If the ratio of the mode and the median of a distribution is 6 : 5, then the ratio of its mean and median is:
- A.
8 : 9
- B.
8 : 11
- C.
9 : 10
- D.
9 : 7
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Correct answer: C
Use the empirical relation between mode, median and mean: Mode = 3 × Median − 2 × Mean
Let the median be M. Given mode : median = 6 : 5, so mode = (6/5) × M.
Substitute into the empirical relation: (6/5)M = 3M − 2 × Mean.
Rearrange to solve for Mean: 2 × Mean = 3M − (6/5)M = (15/5 − 6/5)M = (9/5)M, so Mean = (9/10)M.
Therefore the ratio of mean to median is 9 : 10.