The mean deviation from an average A will be minimum, if A represents:
Median.
Mean deviation from a reference value \(A\) is \(\frac{1}{n}\sum |X_i - A|\). It is a classical result that \(\sum |X_i - A|\) is minimised when \(A\) is the median — moving \(A\) in either direction increases the absolute deviations of more than half the points.
The arithmetic mean minimises the sum of squared deviations (used in variance), not absolute deviations. Mode and harmonic mean have no such minimisation property. Hence the answer is the median.
Similar Questions
If the mean deviation of a set of observations is 15, then the value of quartile deviation is:
If the number of observations in a series is 15, then the third quartile is equal to:
The mean deviation from the average A is minimum if A represents
Important Questions from Mean Deviation
What is the mean deviation about the mean ?
- The mean deviation about median of 10 observations is 15. If each observation is multiplied by $-3$, then find the new mean deviation about median of resulting observations.
Let xi, i = 1, 2, ..., n be n observations and wi = pxi + k, i = 1, 2, ..., n where p and k are constants. If the mean of xi's is 48 and standard deviation is 12, whereas the mean of wi's is 55 and standard deviation is 15, then the value of p and k should be
If the mean deviation 1, 1 + d, 1 + 2d, ..., 1 + 100d from their mean is 255, then d is equal to
The mean of 5 observation is 5 and their variance is 124. If three of the observations are 1, 2, 6, then the mean deviation from the mean of the data is
