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Autograph data

this is a tutorial about the normal distribution power photograph handles it you can see I've got here a picture of some data which actually is a simulation of IQ data with a mean of 100 and one to three standard deviations away either direction just about encompasses all the data the raw data is under here is the normal approximation and this is a frequency diagram so let's see how this all gets to this point and we'll start from scratch so a new page will just double click on the axes because I quite like the appearance of the graph paper which is quite nice alright let's enter some data now you could enter some data from a spreadsheet I'm going to title it IQ data and get a selected distribution instead and use a built-in normal distribution and then I'm going to edit that distribution to have a mean of 100 and a standard deviation of 15 which is pretty much the distribution of data and intelligence tests click OK let's have 1000 of those now create a sample so here is our sample of a thousand values let's sort by X and see what we've got and you can see that the smallest is 49 well 3 standard deviations from a hundred is 315 245 they wouldn't it normally expect much below 55 and the other end above 145 again got a couple of both ends bit over one thing is IQ tests are normally integers so I'm going to use the scaling option here to create an integer value of x but that won't just truncate it that'll make that 49 and 54 and so the mean will be 1/2 less than it should be so I'm going to add 0.5 to that and then scale and there we have it if we also want to have IQ data as the x-axis label I'm just going to right click Edit column header and used IQ Delta there then I can take these two and that would take this information and put it on the x-axis as well okay right there it is right click let's do a dot blot for example it's not groups data so let's do that and that is the good indication of what the distribution is however what I'd like to do is to group it now and you can see that autograph is offering a zero to 200 in classes of 20 that'll do fine but obviously you can adjust all of that continuous or discrete we'll discuss that in a second and click OK it's now ready with all the group options like histogram give me frequency stem-and-leaf and so on so we'll do a histogram and this straight frequency and up now because it straight frequency it's going way off the top and we'll just rescale using the red tick so those are raw data underneath and there is indeed the distribution of talking about now it's it's interpreting this as as continuous data because it goes straight from 60 to 80 over here we have the results box which is full of something I've done before so I'm just going to select that and do backspace to clear it if we do this option here the table of statistics you can see that it gives us 0 to 20 20 to 40 and so on because it's treating the variable as a continuous variable if we use this option here to change it to discrete one thing will happen is that the diagram will move a half to the left because the actual value of 60 goes from 59 and a half to 60 and a half ready it steady there goes you can take a closer look at that but the zooming if you like and you can see that there it is is 59 and 1/2 and now if you do the table of stats we'll see that it does do it correctly is 0-2 19 20 to 39 because and they are correctly being interpreted as discrete data ok let's do some fitting now and right click let's fit a normal distribution so we'll enter probably a distribution normal we're going to fit it to the data so it's going to take the mean of the data which is just a little less than 100 and the standard deviation and what will happen is you should get a diagram that is centered on that 99 let's have a look but it's way down here well you may notice double-click that it's actually been scaled by n already the reason being that the area under a normal distribution in one if you scale it by n the error will be n now the only way we're going to get that to fit the normal distribution is to double click on this and ask it to consider the frequency density option rather than straight frequency so the unit of 1 what this is meaning is that the area of each of these will be equal to the frequency that's inside it now that's about 400 and something here there's a class width of 20 so this is going to go down by a factor of 20 and that will end up the diagram that has an area equal to the frequency n that's just a click OK on that and we can also use our red tick again and now you can see that all the diagrams match you may also notice that the animate objects is available which will animates the class width and you make class width smaller because the total area is fixed to be n it all fits in quite nicely if you go the other way it fits less like it would still represent a total area of n so that's the way to control the normal distribution in autograph there's lots of options but the relationship between the normal distribution and the histogram only really works when the histogram is set to frequency density and one final option we have done is to do the mean and three standard deviations which is this option down here and that's really nice here's your mean and one two three standard deviations either way pretty much encompasses the hold of the data now we can do a few things to tie to this graph up for example it should say frequency density and not frequencies and the double click on the axes label and just you have not d dot while I'm there I think I'll have a look at the pip spacings I think should be at idea that's 2010 that's better and then any object we don't want course evil just pressed on them and question it so the other that's in the railing of exploring how the normal distribution