I've been asked the following question, and, while it is obviously pretty simple, I've got myself in a tangle overthinking it. The question is:
"Imagine that you have data from a web server, which is divided into sessions. You have 24 sessions and for each session you have a number of web-pages visited (the page-count). Suppose the dataset of these counts has sample median of 37.5.
Starting with the original 24 sessions, two additional measurements are added , with page-counts 12 and 38. For the following values, indicate whether or not the median page rank can take that value:
37.5 37 29.25 25.5 25 12
Now I think can be 37.5: if we have 37 and 38 as the middle two values and 11 before 37, then we have a median of 37.5 in the first instance, and if we had 12 and 38, then 37 and 38 remain the middles two values. I was going to say that it cannot be 37, but now the wheels have come off and I'm not sure if it can't be, let alone the others. Does anyone have ideas for how to think about the question in a clear-headed way? My brain has gone to mush!
Note: the calculation for the median according to my textbook is the average of the middle two values if we have a data set of even length and the middle value when it is an odd length.