Let empirical relationship between the three measures of central tendency be a(Median) = Mode + b(Mean), then (2b + 3a):
13
The standard empirical relationship among the three measures of central tendency is \(\text{Mode} = 3(\text{Median}) - 2(\text{Mean})\), which rearranges to \(3(\text{Median}) = \text{Mode} + 2(\text{Mean})\).
Comparing with the given form \(a(\text{Median}) = \text{Mode} + b(\text{Mean})\), we get \(a=3\) and \(b=2\).
So \(2b+3a = 2(2)+3(3) = 4+9 = 13\).
What is the median of the following data?
24, 30, 40, 80, 15, 57, 78, 82, 39, 97, 82