 about. We do that all the way down for all of the data points and here's the related z's and then I can do that for the y's, same kind of things. So the first one is going to be 1 minus the mean this time for the y is 3.67 divided by the standard d for the sample of the y 2.16 is going to give us 1.23 about. We do that all the way down and then we can multiply the z's together to see what the z's together will be 0.8 times the 1.23. We get the 0.99 about. Next one of course would be the 0.27 times the 0.77. We get about 0.21 and so on. Then we just sum up the z's to see what that will be and that'll be the numerator is what it'll be. So if we do that we're going to say let's format this to get the numerator, the sum of the b's. It comes out to 0. If I add up all these column it comes out to 0 and then if I say that the denominator is n minus 1, denominator n minus 1 in 1, 2, 3, 4, 5, 6 minus 1, 6 minus 1 is 5. So 0 numerator divided by 5 denominator gives us of course a correlation of 0, 0 correlation. So that might be surprising. We might say well hey hold on a second no correlation here. If I look at those data sets is that what we would really want to say if we see these data points in real life would we really want to say in our mind that there's no correlation, right? And that's the problem of here because we probably want to say it looks like there's something going on here but then it got hit it got messed up by that one you know data point. So we're gonna say all right if I was to calculate this in Excel we can use the data analysis tool here. If you don't have the analysis tool pack you can turn it on as we do in the Excel practice problem and it'll do the calculation for you. We would just select the data sets looking for the correlation and then we would select the range. I would put labels place it somewhere and then Excel will give us this one and here's the x and the y we're looking at that zero it gives us the zero correlation. This is a static thing here it's not dynamic it will not move as we change an Excel worksheet but it's great to give a preliminary look or a double check. Now note that if I did that again and of course if I eliminated the last data point if I did the correlation for just this down to this data point eliminating the last one we would have a perfect correlation of course it would be one perfectly correlated. So clearly if we were to look at those two data sets we might come to the conclusion that getting a zero correlation might not be exactly right we might want to do some more digging in it. If we were to plot this out we can see the data points here one one two two three three four four five five looks like there's a positive correlation between them but then you've got this zero seven up top which of course skewed our correlation calculation to zero but looking at it pictorially does this line that represents the trend line being exactly straight zero correlation is that what we really want to say about this data where one two three four five data points are in perfect alignment together probably not. So this is just a point that no matter no matter what tool we're using if we just if we just plug this thing into the into the computer using say the data analysis and I get one or I get zero and I say it's totally not correlated at all that might not be that's not the only angle we would want to look at just like all of statistic we don't want to look at it from just one angle typically we would want to then plot it out and say huh well maybe that seems kind of funny maybe there's something else going on here I'd want to drill down into it possibly further than that and obviously you could see that pictorially you can also see it if you do the math over here you would and just look at the data sets and start looking at the z scores it's likely that you might pick up some more information that would that give you some more insights as you as you go through the correlation calculation