If the mode of any data is 36.8 and the mean is 35.37, then the value of median is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 35.85 (approx.)
For a moderately skewed distribution, the mean, the median and the mode are linked by the empirical relation Mode \(=3\,\)Median \(-\;2\,\)Mean. When two of the three are known, the third follows; here the mode and the mean are given, so the relation is rearranged for the median: Median \(=\frac{\text{Mode}+2\,\text{Mean}}{3}\).
Mode plus twice the mean: \(36.8+2\times35.37=36.8+70.74=107.54\)
Median: \(\displaystyle\frac{107.54}{3}=35.846\ldots\), which is about 35.85