Let's suppose i have a class of interval 7, say [20, 27[ With the numbers 20 21 22 23 24 25, there are 2 ways to derive the median yes? I may use [a+b[ /2 to get the median which in the case above will give me 23.5, or i may simply look at the numbers above and clearly see the median is 22.5. So my question is: Are these 2 methods to derive the median valid? I would assume so (since in terms of definition both are valid) but i want to be sure. Thank you :)
What does [20,27[ have to do with { 20, 21, 22, 23, 24, 25 } ? For an interval (with a uniform density function) the median is the midpoint of the interval, yes. For finite set of discrete elements (with no weights on the elements) in sorted order, the median is the middle element. If the number of elements is even, it is usually taken as the mean of the two elements closest to the middle. For {20, 21, 22, 23, 24, 25} the two elements closest to the middle are 22 and 23 and their mean is 22.5. So again, that would be a "yes".
The method of estimating the median from a class (I'm assuming you're referencing the method of estimating the median from a frequency distribution: If not I don't know what you're doing) is simply that, an estimate: the implicit assumption is that the data are spread evenly throughout the class. As your actual (small) data set shows, that isn't always the case. In short: the result you get from using the classes in a frequency distribution should not be expected to equal the actual median.