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Question
The arithmetic mean and mode of a data are 24 and 12 respectively, then find the median of the data.
Solution
Given that the arithmetic mean and mode of a data are 24 and 12 respectively. That is,
MEAN = 24
MODE = 12
We have to find median
We know that
MODE = 3 × MEDIAN - 2 × MEAN
⇒ 12 = 3 × MEDIAN - 2 × 24
⇒ 3 × MEDIAN = 12 +(2 × 24)
⇒ 3 × MEDIAN = 12+ 48
⇒ 3 × MEDIAN = 60
⇒ MEDIAN = `60/3`
⇒ MEDIAN = 20
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