It has been seen that the mean is the arithmetic average of the observations. It is needless to say that average depends upon the size of the individual observations from which they are calculated. If there are a few observations which are quite extreme in their magnitude and are quite away from most of the observations, the value of the mean is either inflated or deflated according to the extreme observations.
As an example, if the period of stay of patients in a ward of hospital is considered, majority of the patients may stay in the ward for treatment from 1 to 15 days. But in few cases, it may happen that they have stayed for one or two months. If the mean is calculated taking all these periods into consideration, the value of the mean will be very high, which may be far from the truth.
Hence the mean as a measure of central tendency, in this type of observations is fallacious. In such cases, the best estimate of the centre would be to locate the magnitude of the central observation. When the centre is thus calculated, there will be equal number of observations with higher and lower magnitude from this central observation (if the number of observations is odd). Median of a distribution is the value, which divides it into two equal parts. It is the value which exceeds and is exceeded by the same number of observations, that is, it is the value such that the number of observations above it is equal to the number of observations before it.
In case of ungrouped data, if the number of observations is odd, then median is the middle value after the values have been arranged in ascending or descending order of magnitude. In case of even number of observations, there are two middle terms and median is obtained by taking the arithmetic mean of the middle terms.
