Efficiency of an Estimator
Among a number of estimators of the same class, the estimator having the least variance is called an efficient estimator. Thus, if we have two estimators and with variances and respectively, and if , then will be an efficient estimator. The ratio of the variances of two estimators denoted by is known as the efficiency of and is defined as follows:
If the value of this ratio is more than 1 then will be more efficient, if it is equal to 1 then both and are equally efficient, and if it is less than 1 then will be less efficient. Let us consider the following working example.
Example:
The variances of the sample mean and median are
and
Find the efficiency of
 The median against mean
 The mean against median
Solution:

Using the formula , we have
e (median, mean)
Therefore, the efficiency of the median against the mean is only 0.63. This means that a sample mean obtained from a sample of size 63 will be equally as efficient as a sample median obtained from a sample of size 100.

Using the formula , we have
e (mean, median)
Therefore, the efficiency of the mean against the median is 1.57, or in other words the mean is about 57% more efficient than the median.