Median
Arithmetic mean is the central value of the distribution in the sense that positive and negative deviations from the arithmetic mean balance each other. It is a quantitative average.
On the other hand, median is the central value of the distribution in the sense that the number of values less than the median is equal to the number of values greater than the median. So, median is a positional average.
Median is the central value in a sense different from the arithmetic mean. In case of the arithmetic mean it is the “numerical magnitude” of the deviations that balances. But, for the median it is the ‘number of values greater than the median which balances against the number of values of less than the median.
Median for Raw Data
In general, if we have n values of x, they can be arranged in ascending order as:
x1 < x2 < … < xn
Suppose n is odd; then the median is the (n+1)/2 th value.
However, if n is even, we have two middle points
Median for Grouped Data
Identify the median class which contains the middle observation (N+1)/2 observation. This can be done by observing the first class in which the cumulation frequency is equal to or more than (N+1)/2
Here, N = Σf = total number of observations.
Calculate Median as follows:
Where,
L=Lower limit of median class
N=Total number of data items = ΣF
F=Cumulative frequency of the class immediately preceding the median class
fm =Frequency of median class
h=width of median class
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