In a moderately asymmetrical distribution, the mode and mean are 31.5 and 34.5, respectively. Calculate the median:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 33.5
In a moderately asymmetrical (moderately skewed) distribution, the three averages follow the empirical relation: Mode = 3 Median − 2 Mean.
Putting the mode 31.5 and the mean 34.5 into the relation: \(31.5=3\times\text{Median}-2\times34.5\)
\(3\times\text{Median}=31.5+69=100.5\)
\(\text{Median}=100.5\div3=33.5\)
Tip: In such a distribution the median lies between the mode and the mean. Here it must lie between 31.5 and 34.5, and 33.5 is the only option there; 100.5 is three times the median, the value before the last step.