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 quantitative average.
On the other hand , median is the central value of the distribution in the 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 the 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
If n is odd then Median=\[(\frac{n+1}{2})^{th}\] value
if n is even then Then we have two middle points Median=\[ \frac{(\frac{n}{2})^{th} value +(\frac{n+1}{2})^{th} value}{2}\]
For example
Example:
The height (in cm) of six students in class are 160, 157, 156, 161, 159, 162. What is median height?
Solution:
Arranging the heights in ascending order 156, 157, 159, 160, 161, 162,
Two middle most values are the 3rd and 4th
Median = 0.5(159+160) = 159.5
