 and then we're going to say this needs to be currency and negative numbers bracketed and then no dollar signs and let's keep the decimals okay and then for some reason I pasted this in column C I wanted to paste it in column A so I messed that up I'm all out of whack today for some reason I'm going to select column A and B and delete those right click and delete okay now we're going to do the mean calculation which is the average equals the average tab and I'm just going to select the data set I could do that by selecting the drop down just this way boom dancing ants doing their average dance dancing ants doing the average dance and then we're going to do the standard deviation equals standard D standard D for the population and we'll select the whole data thing again and now they're doing their standard D dance and then we're going to do the median equals the median that's the one in the middle and we'll select that and then boom and in the mode isn't always useful but for some data sets the mode is the one that occurs most often so if you're talking about data sets with whole numbers like this the mode might be useful as the one that's going to be occurring more often so this equals the mode let's do a single mode I'm only in the mood for one mode and then there we go so now you can see the mean is quite similar to the median which is an indication that it might conform to a bell curve that we can approximate with a formula for the bell curve the mode is also quite close which again is another indication that we might be able to approximate this with a bell curve so let's now create the data now I could also create a histogram just to see this I'm going to put my cursor on the title this time control shift down and then control backspace to get back up and then go to the insert charts histogram let's insert a histogram so there we have it and it looks you'll remember that with the histograms we have our buckets on the bottom with the lower limits and the upper limits and we're seeing how many times these items fall into these buckets so as we would expect this middle point around the mean has the most of our data points falling within it so the shape of this looks somewhat like a bell curve type of shape we can see that the mean is similar to the median and the mode is also similar all indications that we might be able to use an actual bell curve formula to approximate this information so if we look at this middle point for example the heights of the pitchers on average are like 74 if we divide by 12 inches because this is an inches to get it in feet we're talking 6.17 so I'm probably not going to be a pitcher unless but I can like practice I can practice really hard though and I'll make up I'll totally make up the difference but whatever so now we're gonna now that we have that now we're gonna say let's plot the actual bell curve because that might give us some predictive data to do that we want to see how many what's the X's do I do I need to be approximating in other words if I was gonna go over here and say that I want to have X and then P of X to plot my bell curve on these data points are gonna make this black white I'm gonna wrap it and center it should I should I just start my X's at one and go up to like 100 inches I might not need to do that because because it's likely that when you're talking about baseball pitchers that because it's a specialized area that they're gonna have a pretty idealized or somewhat grouped together body type in order to maximize you know that level of performance right so you would think that where should I start to graph on the X let's let's think about it we could say well if I have my my number of standard deviations away of four that's gonna include almost all of the data remember that in theory the bell curve goes on forever but four standard deviations picks up the vast majority of the data so so let's take four four standard deviations up and below from the mean how can we do that will lower X and upper X would then be lower X is gonna be the mean plus the standard deviation notice it's only 2.3 inches on the standard deviation so this should be lower this should be minus minus the 2.3 times four because there's so four times the standard deviation minus that middle point will give us our lower limit which is only 64 48 and if I divide that by 12 this divided by 12 you're as small as the 5 37 so then we're gonna say but that's way there's not many pictures that are gonna be done but any case we're gonna say then this one is gonna be the mean plus the 2.3 times to four standard deviations and that's gonna give us the 82 92 if we divide that by 12 this divided by 12 you got 6.91 okay so then we're gonna say alright then we're going to say let's go ahead and create our X's here starting at the low point I'm just gonna use whole inches not fractions of inches so I'm gonna start at 64 and then we're gonna go up let's make this a little larger I don't need the decimals here so I'm gonna get rid of the decimals 64 and then 65 and I'm gonna get rid of the decimals there selecting those two fill handle dragging that down until I get to 83 so I'm gonna drag it down till I get to that upper 83 don't have to go that far because again you would think that the picture range would be somewhat you know packed packed together given the nature of heights of pictures and what they're doing so then we're gonna say the norm dot this this equals the norm dot dist and we're gonna say the X this time I'm gonna do the spill array because last time we did we did the absolute reference stuff so if I take this X and say control shift down picking up all the data control backspace back up to the top now I have an array of all my X's the mean is gonna be here which I still have a tendency to want to make absolute but we shouldn't need to because we're now doing an array which is just gonna spill out the data comma the standard deviation is the 2.3 comma cumulative or no we do not want it to be cumulative because we're taking the the approximation or the likelihood of each individual point so I can put I can put false or zero and then close up the brackets and then enter and it spills out and we're lucky we closed it up before we we spilled it because then we spilled it and then it didn't spill as much because you put the cuz we closed it I don't know what I'm talking anyway so we're gonna go to the home tab and let's percentify number group percentify and then