Calculating median category


Fortran must die
I have ordered categories (e.g., 0-3 months, 4-6 months) and the number of customers who were in each category (say 45 in the first 50 in the second, etc). To chose the median category I added up the total number of customers in all categories, found the middle value and then found which category that customer would be in. So for example if the categories were 0-3 months, 4-6 months. 7-9 months, and 10-12 months and there were 25 in the first 25 in the second, 25 in the third and 26 in the fourth I added these up (101 customers, saw that 51 was the median) and found out that category 3 7-9 months would have had this customer.

So I said that the third category was the median one, but I am not sure if that is valid way to analyze data. What makes it worse is the categories do not have the same length of months. So the first four have 3 months each, the next 3 categories 12 months, than the next 2 have five years each.

I am actually answering the following question by seeing if the two groups in question have different medians (calculated as above). It would be better to know the median or average months for all customers, but I do not have this information.

a. Is there a significant difference in the time from development of the IPE to closure of the service record for all individuals with the most significant disabilities when compared to youth with the most significant disabilities? If so, to what does the VR agency attribute this difference?