Sampling Distribution of Median

Definition: The Sampling Distribution of Median shows the distribution of sample medians, a mid-value in the items arranged in some chronological order in the sample drawn from the population.

If the population is large approximated by the normal distribution with mean? And a standard deviation σ, the medians of random samples of size n are distributed with mean? And a standard deviation 1.2533σ/√n. The sampling distribution of the median is likely to be normally distributed when the sample size ‘n’ is large.

The standard deviation of the distribution of sampling median is called as the standard error of the median and is expressed as:

sampling distributionm of median and sample standard deviations-1Thus, it is clear from the above explanation that the expectation of the median is same as that of the mean, but the standard error of the median is 1.2533 times of the standard error of the mean.

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