What is the formula in getting the median of a grouped data?

Answer 1

The median is a "midpoint" - for a set of numbers, it is the value for which half are above and half are below. Averages can be thrown off by extreme values, but medians are less susceptible. To calculate it, take your set of numbers, and arrange them from smallest to largest or vice versa. If you have an odd number of values, your median is just the one in the middle; if you have an even number, it's the mean of the two in the middle. So, the median of 1, 3, and 6 is 3, and the median of 1, 100, 101, and 102 is the mean of 100 and 101, or 100.5 . If you have values x1, x2, ..., and xn (n is a positive integer) where they are arranged in numerical order (either xi <= x(i+1) for i = 1, 2, ..., n-1 -or- xi >= x(i+1) for i = 1, 2, ..., n-1), a simple formula to calculate the median is to first determine if n is even or odd. If odd, just return the "middle" value - i.e., xj where j is n/2 rounded up to the next integer. If n is even, simply take the mean of xk and x(k+1) where k = n divided by 2.