 because we're looking at that top one which is 79 minus the 127, 127.08 divided by the standard deviation of 11.66 gives us four standard deviations away over that because we went to 79. So there we have it and we can do that all the way down. Those are going to be our Z scores. Now of course when I look at the data sets here I can't really compare the height versus the weight because they're different units. What we can compare then is I can see if there's a relationship by looking through the Z scores and see if there's a relationship as we compare the Z scores. So let's do that over here. So what I'm going to do is I'm going to take my data I'm going to take the one that is going to be this one first with the weights because there's more data points here and so I'm going to put that one on the left this time and then I'm going to put the heights on the right. So here's the data set my headers didn't pull over for some reason but here's my height data sets with the 60 and and so on I'm sorry this is still the weight so I'm copying this over but I'm just putting the the weight first so this is the same thing as the weight here with the weight the normal distribution and the Z score and I'm going to compare that to the height. So here's the height data and here's the the the norm.dist and there's our Z score for the height. Okay so now what I did is I tried to match up the the the Z scores so that 4.20 is close to the 412 and then the next Z score if I go down to the next Z score it's at the 3.68 which is close to the 3.87. See what I'm doing here I'm trying to match up the Z scores and the next Z score is at 3.15 and I tried to match that up I think when I copied this over it got staggered a little bit but I tried to match that up to the relative 3.15 on the left which is actually down here so we've got we've got something like this one so it actually lines up to this one and then I'm taking the difference so I'm saying this is close to that Z score let's take the difference between this 90 minus the 62 and I get a difference of 28 right and on this one this Z score of 3.68 is close to like 3.69 and so I took the difference of this 84 that's related to this Z score 3.69 is 84 minus this one of 61 and that gives me the 23 and then I went down and said okay this Z score is close to this is the 2.63 it's getting quite staggered here but 2. it's close to this 2.67 so then I took the 2.67 has the related 96 to it minus the 63 and we have a difference of the 33 so all I'm doing is matching up the Z scores as best I can between the two data sets and then looking at the difference between the the the actual measures which are measured in pounds for weights and in inches for the heights and so to see if there's a relationship between the Z score and the difference between those intervals see if it was just a direct conversion as we saw with the perfect correlation type of thing with the distance the difference between inches and feet would always be 12 it would be a you know a multiple of 12 right so we'd see a trend when we start to be comparing these so I did that all the way down here and then I squished them together so now they're on one so these are all of my differences that I found for related Z scores and then if we plot that out this is this is the plotting actually of the bell curve for the height this is the bell curve for the weight and this is me plotting out this list of numbers which you can see there's a relationship between the numbers right you can see kind of a trend from the Z scores so the idea here would be that is to get kind of an intuitive sense of the idea that it's that Z score which is the thing that helps us to do this comparison and it's the Z scores which are a prime a huge part of the calculation for the the correlation as we could see over here so it's useful then to get to sometimes to focus in on those Z scores a little bit more as a way that possibly can give you some better understanding of what's actually going on within the datasets