  # Median

<p>Every book/guide I've seen says the median is the middle value. Fine, I get that, but it's never that simple. If you have a graph, you have 2 values - x and y - how do you find median y or median x? Same Q for tables.
This is like the only problem I have in math, it's kind of annoying.
Thanks for any help :)</p>

<p>You are right -- the concept of a median is so straight-forward that they have to give you other hoops to jump through. They often present the data on a chart or (less often) an x-y graph for paired data (like number of boy vs # of girls in a club over a period of years).</p>

<p>Safest way is often to pull the data out of the table or graph and make your own list, in order, including multiples. Then finding the median is easy again.</p>

<p>Yes, but for example, in the May SAT, I got the statistics question wrong, and it asked: what is the median gas mileage of the x-y graph above? It had gas mileage on the x-axis and number of cars on the y-axis. So how do you do that one?</p>

<p>I'm a terrible teacher, but bear with me.</p>

<p>let's say:</p>

<p>5 mileage = 40 cars
10 mileage = 70 cars
15 mileage = 35 cars
20 mileage = 50 cars
25 mileage = 70 cars</p>

<p>just imagine that info in graph form.</p>

<p>What I like to do with this type of question is take the number cars. The total number would be 265.</p>

<p>Now divide by 2 and find the median of that. It would be the 133rd car.</p>

<p>Just plug it into the graph, either from the top or the bottom. Both would reveal that the 133rd car is located in mileage C.</p>

<p>So the answer is simply mileage C.</p>

<p>Nah I got your explanation perfectly. So you're saying that the median one is the median car projected on the mileage axis? As in the car in the middle, projected on the gas mileage. No need to order from increasing to decreasing or whatever? Or should the gas mileage be increasing for this to work? (As in a<b<c<d<e)</p>

<p>On graphs, the gas mileage will always be pre-ordered from smallest to largest (a<b<c<d<e) because it simply makes sense for the x-values to increase from small to large (I guess it could also be in decreasing values, but then you'd just need to reverse it).</p>

<p>I'm not sure what you mean by "median car projected on the mileage axis," but when you are calculating median all you need to do is find the median "rank" and locate the corresponding car when the data is organized in either ascending or descending order. You don't actually need to create a list of all the cars and their mileages and cross out each end, especially when you have a large set of data.</p>