Median

0:00- [Instructor] In this video, we're gonna talk more about what it means to have a typical value for a set of data points. Now, when we say typical, we typically... We typically, I'm not overusing the word. We're talking about some indication of where the center might be.

0:17Now, we've already seen things like the mean where we could add up all of these numbers, and then divide by the number of numbers, which in this case is seven, and that would definitely be an indication of the center, may be an indication of what's typical. But that can be very sensitive to what's known as outliers.

0:36For example, if this 5 points, this is a lot lower than all of the other values, that would drag the mean down. If that 5 were 0, it would drag it down even more. That 5 were a negative 5 million, it would really drag it down. And so, there's a question is whether there could be another measure of central tendency or center that is not as sensitive to outliers.

0:58And the simple answer is yes and it's called the median. And to calculate the median, what we do is we write all of the numbers in order and the median will be the center of those numbers. So let's write all these numbers down. So the smallest of these numbers is the 5 points and I'm keeping track.

1:17So we have 5. Then, we have 12 twice, let me mark those. We have 12 twice. Then, we have a 14, 14. Then, we have 17 twice, 17, 17. And last but not least, we have 20. So it's very important you have to order them. You just don't arbitrarily take the middle of the numbers.

1:44You have to order them, and then take the middle. And the middle here is we have seven numbers, so whichever number has three on both sides is the middle. So this right over here is the median. And what's useful here is even if this 5 were 0, it's not going to change the median.

1:59Or even if this 20 were 200 or 2,000, it's not going to change the median. So a big takeaway is use the median if you want it to be less sensitive to outliers. Now, with that done, or now that we understand that, let's look at another example. So here, we are given another data set, daily steps walked over six days.

2:21Why don't you pause this video and try to figure out what the median is? All right, so same idea. Let us actually... let us actually order these. The least number of steps is 3,000 right over here. Let me cross that out. So we have 3,000. Then, we have 4,000 twice.

2:42So 4,000, 4,000. Then, we have 5,000, 5,000. Then, we have 6,000. And then, last but not least, we have 22,000. That one feels a little bit like an outlier. That seems not as typical as everything else. Everything else is 3 to 6,000 and all of a sudden we have this big jump here.

3:06But which one is the middle value? Well, this is a little bit trickier because we have six data points. There is no exact middle. We could say that the middle is right in between 4,000 and 5,000 or we could say that we have two middles, 4,000 and 5,000. And the way that mathematicians, statisticians have defined the median in this case is just to take the exact middle between 4,000 and 5,000 or to take the mean of 4,000 and 5,000 which is 4,500.

3:36But once again, this is not sensitive to outliers. If this 22,000 were just 6,200, we would still have the same median. If this 22,000 were 22 million, we would still... That would be a lot of steps to walk over six days. You'd be walking very far and very fast.

3:54You would still have the same median. So medians are good when you're concerned about not being too sensitive to outliers. Well, if this was 22 million steps, that would dramatically change the mean and it would be a mean way higher than any of these other values, other than the 22 million.