How To Calculate The Median - Ungrouped Data
This VideoJug film is designed to show you a few examples of calculating median. So follow along as we guide you through the process of calculating the median.
Hi, I'm Dr. Shah. I was the National Lecture Competition winner in 1999, and I'm the math master at Mathscool.
Now, ready for a new way of doing math? Now, there are three different cases in which we'd need to calculate median. The first case is if we have a list of data. The second case is if we have a table of un-grouped data.
So that would probably be discrete data, something like the number of times you entered a cinema, or the number of seats in a car, things that can be 3.12 something like that. And then three, a table of grouped data, and the method we'd use would be different for each of these.
Our second case is when we have a table of un-grouped data so like this. This might be players in a poker tournament and these are the number of wins. Say 12 people didn't win any matches, 27 people won 1 match, 25 people won 2 matches and so on.
So, this is a table of data and the method we use to find in the median. In this case, it's different. We'd have to re-write the table to a cumulative frequency table.
So our cumulative frequency table is going to have the same thing on the top, I'll just call it X to abbreviate it; 0, 1, 2, 3, 4, and at the bottom is going to have cumulative frequency, and we use the letter capital F for cumulative frequency. So if you see the capital letter F, you know it's referring to cumulative frequency. Cumulative frequency means the running total of the frequencies.
So up to here, the frequencies are only 12, but by the time I get to here, I've got to add both of those together. So that's going to be 39, and then now adding that one on. So all three of these is going to be 64, adding this one is going to give me 77, and adding that one on is going to give me 79.
So that's my running total of the frequencies, cumulative frequencies. Now, this last number in the total number of frequencies is N. Which is, in our last example, is how many pieces of data we had.
And it makes sense because it's the sum of all these people, we and so therefore we know there were 79 people taking part in that tournament. And as before, to find the median we want half N plus 1. So if N equals 79, 79 plus 1, times a half will give me 80, divided by 2 is the 40th value.
So we want to find the 40th value, so we look along these cumulative frequencies until we find the number 40. Now you can see that the number 40 isn't in our cumulative frequencies so, do we choose this one here which is close to 40 but not quite 40, or do we choose this one here which is way above 40? The answer is, it's not which is closer to 40. If you can't find 40 in your cumulative frequencies, you must look for the next number above 40.
So in that case, it would be this number here 40 and read up to here to find your median. So in this case, the median is two. .