 out on a histogram. If we just select all of the age and put it on a histogram, it looks like this. So it's kind of a chaotic histogram. It's not exactly bill shaped. It's, it's a, you know, kind of, you got the, I guess the middle point here, but we have another peak at 30 to 31. And it's kind of interesting in baseball because experience might matter in baseball more than in other sports. In other words, sometimes when people temper down and actually get less edgy, they might actually do kind of better sometimes because of the, of the nature of baseball. You need a lot of patience, you know, with baseball. But then we've got the batting averages, which looks kind of more like a bell shaped curve, which is somewhat what we would expect with the batting averages. So we just selected this whole thing and entered a histogram and notice batting averages are kind of like performance. It would be kind of like performance on a test. And you would think that if you, if you were picking people that were all the best based on their performance of being the best that if you took like the test scores of it, meaning judge their performance, you'd get something that looks somewhat like a bell curve. If you didn't get a bell curve in that case, you might think that something funny is going on because you would think that they're all similarly, similarly good in terms of their performance because they're all at the same level, they're professionals. So you would think that performance would, would mirror some kind of bell curve possibly. So if it wasn't a bell curve, you might, that might lead to interesting questions in and of itself. Now, if I take the mean of the data, hold on, if I take the mean of the data, we just select all of this data and take the average, adding up all the ages and divided by the number we get to 28. If we take the batting average mean, adding up all the batting average and divided by the number of rows, we get to the .22 or 22%. In other words, notice that's under 50% well under, of course, because like I say, it's, it's a lot more likely that when someone is batting that they're going to get out that the then they're going to get on base at some and some way, then the standard deviation of the sample for the ages, this is the measure of the spread 3.66 and for the batting average .0555. So then we have our, our correlation calculation. So let's just do this in terms of the mathematical calculation for the correlation. We take all of our ages, and we're going to come take the Z score. So the Z score, we've seen multiple times, I'll just calculate that it's going to be the 24 minus the 28 divided by the standard D 3.66. And that gives us 1.08 about there's rounding involved here. Let's just do another one. And so we get the 25 minus the 28 divided by the 3.66, we get the 81 about. And then we can do that all the way down. We can do that for the second factor, which is the batting average, where we can take then the .5 in this case minus the mean .2216 divided by the standard D for the sample .0555. We get about five. We could do that all the way down. Hold on, we get about five. There it is. And then we could do that all the way down. And then we can multiply out the two Z scores. So now we're going to multiply out the 1.08 times the 5.5 .01. That gives us the 5.43 about. So that gives us these two bits, which we can now sum up. And if we sum it up, that will give us our numerator. So if we sum all that up, that gives us the 41 31 the numerator, the denominator is the number of items minus one. So we'll do a sub calculation for that in minus one in the number of rows minus one is going to give us 814. Then we can divide out the numerator and the denominator. Now in the outer column being 41.31 divided by 814 gives us about .0507 and so on. Alright, so it's not highly correlated here, the age and the batting average. So we can kind of start to think about that and say, well, maybe that's the case because like I say, if someone is in the league longer, then maybe their batting average, they get better possibly at batting and they've done more steroids by just kidding. So they might have bulked up in that time or something, but no. So the performance could go up in baseball. But if I take my data tab over here and we test that out by going to my data analysis, which you can turn on in Excel by going to the options and turn on the analysis toolkit and go to the data analysis looks like this, we can check out the correlation, enter the data, which would just be the two columns of data, which have to be side by side. So you couldn't take this just from the original data set. We had to put them side by side if we're going to use this analysis tool for the correlation. And that would then give us the age versus the batting average. There's that negative .05075. So there's our double check that we did on our numbers. If I was to then plot it, the age on the X, the batting average on the Y, you could see that the trend line