How To Calculate The Median - List of Data
To find the median in a list of data, arrange the data
Hi, I am Doctor Shah. I was the National Lector Competition winner in 1989, and I am the maths master at Mathscool. Now, ready for a new way of doing maths? Now, there are three different cases in which we would 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 ungrouped data, so that would probably be discrete data; something like the number of times you enter the cinema, or the number of seats in a car- things like that, things that can not be three point one two, or something like that. And then three, a table of grouped data. And the method we would use, would be different for each of these. So, let us start with the first case- a list of data. So, if I have a list of data, I am going to start off with a list of some data here on, maybe this could be, the number of cans of coke drunk in a month by some students. So, I have got this data here. The first thing I need to do with this data is to place it in numerical order, so I need to order the data. So, looking at my data, the smallest value is twenty, so I am going to put that first- twenty two, twenty three- I think I have got two of those, there is twenty four here, two twenty sevens, two twenty nines, and a thirty. So, our first step is to list the data in numerical order. Once we have done that, we want to find the median, which is the middle one in the numerically ordered list. Now, here I have got one, two, three, four, five, six, seven, eight, nine, ten pieces of data- and you might think that the middle one would be the fifth one, but that is wrong. One, two, three, four, five- there is the fifth one. If I move that down, and you count how many are to the left of it- one, two, three, four- and how many is on the right of it, one, two, three, four, five- you can see it is not actually in the middle. So, if you have worked out how many items you have in your data, that would be called 'n'. Then the median would be a half 'n' plus 1th value. So, in my example, 'n' is ten- there are ten numbers there, so 'n' is ten plus one, times a half, so it is eleven divided by two, is the five and a ½th value. Well, one, two, three, four, five- my fifth value is twenty four, and my sixth value is twenty seven- so my five and a ½th value would have to be halfway in between those. So, halfway in between twenty four and twenty seven- add them up, twenty four plus twenty seven, divided by two, and that gives me twenty five point five as my median. Now, twenty five point five is not any of the numbers in the list of data, but you can see it would be the median, because if I chose twenty five point five as my median- then, one, two, three, four, five would be less than it- and one, two, three, four, five would be more than it. That is our first case- finding the median for a list of data. .
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