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
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
The observations 4, 1, 4, 3, 6, 2, 1, 3, 4, 5, 1, 6 are outputs of 12 dices thrown simultaneously. If m and M are means of lowest 8 observations and highest 4 observations respectively, then what is (2m + M) equal to ?
The mean of the series x 1, x 2… x nis X̅. If x 2 is replaced by λ, then what is the new mean?
The mean of a group of 100 observations was found to be 20. Later it was found that four observations were incorrect, which were recorded as 21, 21, 18 and 20. What is the mean if the incorrect observations are omitted?
