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 \(2b+3a = 2(2)+3(3) = 4+9 = 13\).
Important Questions from Measures of Central Tendency
If X̅ = 20 is the mean of 10 observations x1, x2, ... x10; then what is the value of \(\displaystyle \sum_{i=1}^{10}\left(\frac{3 x_i-4}{5}\right) ?\) ?
What is the mean of the numbers 1, 2, 3, ... 10 with frequencies 9C0, 9C1, 9C2 ..., 9C9, respectively?
Which one of the following measures of central tendency is used in construction of index numbers?
The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is
The ‘less than’ ogive curve and the ‘more than’ ogive curve intersect at
