![]() I have this long tail to the left, it's likely Median is referring to that, the mean is referring to this. Is me approximating it, but this would roughly be our mean. And so our balance point is probably going to be something closer to that. Wanted to balance this? Well, we have equal areas on either side, but when you have this long tail to the right it's going to pull the mean to the right of the median in this case. The fulcrum, or what does our intuition say if we Symmetric distributions? Well let's think about it over here. And that all comes out of this idea of the weighted average of all And so you could put a little fulcrum here and you could imagine that this thing would balance, this thing would balance. It in terms of physics, the mean would be your balancing point, the point at which you would want to put a little fulcrum and you would want to balance the distribution. So this is going to be your mean as well, this is going to be your mean as well. Your mean and your median are actually going to be the same. But what about the mean? Well the mean is, you takeĮach of the possible values and you weight it by their frequencies, you weight it by their frequencies and you add all of that up. So that's the median for well behaved continuous distributions like this, it's going to be the valueįor which the area to the left and the area to the right are equal. Longer it's much lower, this part of the curve is much higher even though it goes on less to the right. Similarly, on this one right over here, maybe right over here, and once again I'm just approximating it,īut that seems reasonable, that this area is equal to that one, even though this is And if that is the case, then this is going to be the median. Say that the area here looks pretty close to theĪrea right over there. Once again, I'm approximating it, but it's reasonable to Little bit over to the right, this maybe right around here, To go right at the top of this lump right over here,īut if I were to do that it's pretty clear, even eyeballing it, that the right area right over here is larger than the left area. Going to be super exact, but I'm going to try to approximate it. We would want to think,Īt what value is the area on the right and theĪrea on the left equal? And once again this isn't Non-symmetric distributions? Well we'd want to do the same principle. Another way to think about it is, the area to the left of that value is equal to the area to the right of that value, making it the median. Is right over here, and so this value, onceĪgain, would be the median. More unusual distribution, this would be calledĪ bimodal distribution where you have two major lumps right over here, but it is symmetric. And in general, if you have a symmetric distribution like this, the median will be right along that line of symmetry. So in looking at a density curve, you'd want to look at the area, and you'd want to say, OK, at what value do we have equal areaĪbove and below that value? And so for this one, just eyeballing it, this value right over Values are above that value and half of the values are below. Want to find the value for which half of the If we have a set of numbers and we order them from least to greatest, the median would be the middle value, or the midway between Median for the data set described by these density curves. Want to think about is if we can approximate what value would be the middle value or the And we have four of them right over here, and the first thing I But what I want to talkĪbout in this video is think about what we can glean from them, the properties, how we canĭescribe density curves and the distributions they represent. ![]() Videos we introduce ourselves to the idea of a density curve, which is a summary of a distribution, a distribution of data, and in the future we'll also look at things
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