We've been able to figure out what the mean is. So we take each of the data points and we figure out, what's its absolute deviation from the mean? So we take the first two.

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So we say, two minus the mean. Two minus the mean, and we take the absolute value. So that's its absolute deviation. Then we have another two, so we find that absolute deviation from three.

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Remember, if we're just taking two minus three, taking the absolute value, that's just saying its absolute deviation. How far is it from three? It's fairly easy to calculate in this case. Then we have a four and another four. Let me write that. Then we have the absolute deviation of four from three, from the mean. Then plus, we have another four. We have this other four right up here.

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Four minus three. We take the absolute value, because once again, it's absolute deviation. And then we divide it, and then we divide it by the number of data points we have. So what is this going to be? Two minus three is negative one, but we take the absolute value.

It's just going to be one. Two minus three is negative one. We take the absolute value. It's just gonna be one.

And you see that here visually. This point is just one away. It's just one away from three. This point is just one away from three. Four minus three is one.

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• Absolute value of that is one. Four minus three, absolute value. That's another one. So you see in this case, every data point was exactly one away from the mean. And we took the absolute value so that we don't have negative ones here. We just care how far it is in absolute terms. So you have four data points. Each of their absolute deviations is four away. So the mean of the absolute deviations are one plus one plus one plus one, which is four, over four. So it's equal to one. One way to think about it is saying, on average, the mean of the distances of these points away from the actual mean is one.

And that makes sense because all of these are exactly one away from the mean. Now, let's see how, what results we get for this data set right over here. And I'll do it Let me actually get some space over here. At any point, if you get inspired, I encourage you to calculate the Mean Absolute Deviation on your own.

So let's calculate it. Well, let's figure out the absolute deviation of each of these points from the mean. It's the absolute value of one minus three, that's this first one, plus the absolute deviation, so one minus three, that's the second one, then plus the absolute value of six minus three, that's the six, then we have the four, plus the absolute value of four minus three. Then we have four points. So one minus three is negative two. Absolute value is two. And we see that here. This is two away from three.

We just care about absolute deviation.

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We don't care if it's to the left or to the right. Then we have another one minus three is negative two. It's absolute value, so this is two. That's this. This is two away from the mean. Then we have six minus three. Absolute value of that is going to be three.

And that's this right over here.

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We see this six is three to the right of the mean. We don't care whether it's to the right or the left. And then four minus three. Four minus three is one, absolute value is one. And we see that.

It is one to the right of three. And so what do we have? We have two plus two is four, plus three is seven, plus one is eight, over four, which is equal to two. So the Mean Absolute Deviation Let me write it down. It fell off over here. Here, for this data set, the Mean Absolute Deviation is equal to two, while for this data set, the Mean Absolute Deviation is equal to one.

And that makes sense. They have the exact same means. They both have a mean of three. But this one is more spread out. The one on the right is more spread out because, on average, each of these points are two away from three, while on average, each of these points are one away from three.