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# Find the median for each list of numbers.$27,35,39,42,47,51,54$

## 42

#### Topics

Multivariable Optimization

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### Video Transcript

this question gives you a list of numbers and asks you to find that the median the list, which is already in order, goes 27 35 39 42 47 51 and 54. Now a median is the point in, essentially in the middle of your data, the median point is defined as the point where the amount of data that's greater than the median is the same as the amount that's less than the median. So we have a list that's already in order like this. It's pretty easy to find the media. We just need to know which one is in the middle. One way we can do that is we can just cross off the first and last as we dio and we'll eventually reach one or two and find that 42 is our median. But another way to do that in a way that it is a lot faster when you have bigger sets, is to figure out how many total data you have. You have here seven data points and you want to find what's going to be the middle of the first data point in the last data point. So you have one on one end. And yet 10.7 on the other end, and you want to find what's in the middle? Well, the midpoint of one in seven is gonna be one plus 7/2 or 8/2 or four. So it's gonna be your fourth data point. Is your medians at 123 four. Oh, your median here receives 42. And that's a formula that we, uh we can use a lot say, if we have n data points are median is the end plus one thing over tooth in the n plus one over to position. Um, so here are median is 42 and that is your final answer.