Math 221 Lesson 04 five number summary

all right have an excel file here and actually i've done few things to it but before do that let me talk about where this file came from this came from sheffield.ac. uk mash statistics data sets honestly don't mean grabbed this because thought this would be data set that could use in my classes and to do that wanted to first start off by by setting this up and so there's person id there's head circumference this data set basically has some information on children that were born have some measurements don't really know where the children are who they are there's some associated id but there's head circumference there's length birth weight gestation period for the pregnancy the mother's age at time of birth the father's age at time of birth there are more variables in here but just distilled it down to these so that we could do few of these exercises and over to the right we'll start column describes there's the mean mode sum of squared sample variables and then letting excel compute the sample variance they're just sample standard deviation and again letting excel can be the standard deviation so you can check our work and this is set up so that students can they can be able to count compute these by hand have better understanding of how these work and also created these whisker plots and we'll go through each of these and i'll show you few shortcuts too so first of all there we have this the head circumference is already done so let's start working on the length and column let's compute the deviations from the mean and so like if we look at baby 13 13 when he or she was born this baby was 17 inches long and how does that differ from the mean we can use formula to describe that column has length there's nothing else in it if go to this go to the very top put control down that brings the bottom of the data set control down one more time and the very bottom of excel means there's nothing else in there okay so let's compute the deviation from the mean the formula is equals i'm going to click on the cell next to it you could type in e2 but like you let the mouse it's nice when you let excel do as much of that work for you as possible so e2 minus the mean the bar means the arithmetic average the arithmetic mean so and the formula for that is average and could type in another thing could do is just click on this thing right here and the proper thing to do would be to close it off with parenthesis and but if you don't want to close it off with parenthesis if you leave it there you hit enter excel will ask you does this look right you enter again so now we have the deviation from the mean is negative 2.929 and if you want to copy that all the way down for the column where you have this all selected there's little box to the right you double click that thing right there and that will compute to the deviations of the mean for each of the observations of the the baby length that time of birth and then the next thing we do is we square the deviations and we'll use that to compute the standard deviation eventually but it's one of the steps in there and you'll notice in column you have minus bar and this you have that same thing in parenthesis squared and so we you can recompute all of that but you can just use information to the left which we'll do there's two ways you can do that you can do equals you click on that cell put in the multiplication sign the shift 8 f2 so f2 times f2 that gives you the deviation squared you could also do equals f2 and then use little carrot squared it's the same thing and so that gives us our deviations squared let's come over here the length we can compute the mean start filling out this table you want to compute the mean that's equals average and that's let me double check yes it's column so it gives us that we're looking at that's why that's wrong there's some okay the difference from the mean for each of those observations of course would be zero but the the average length the arithmetic mean length is 19.929 inches the mode you can do the same thing actually i'll show you little way you can cheat let's just copy that down ctrl is copy i'll paste that in there then i'll come up into the formula bar and change where it says average and type in mode so the most common length at birth among this data set is 20 inches the sum of squares so let's add up all those square deviations and that is believe just called yeah so column i'm going to select you could put in colon so now we have the sample variance so and that's the sample of variance gives it well can copy this formula over here but the sample variance is the the sum of squares divided by the count observations we have that was in column minus one your population variance you don't give the minus one but that minus one means for the sample variance gives little bit of penalty greater proportional penalty for smaller data set and smaller proportional penalty for larger data set so we have our sample variance of 1.23 and you can also use the formula equals var dot that's sample variance and we're looking at and so hopefully those will both be the same and looks like they are and you find the sample standard deviation you take the square root of that the square root of the sample variance to give you the sample standard deviation 1.13 you can check that dot is sample standard deviation we're looking at everything in row and the values are the same well let me show you shortcut yeah before we do that let's start working on these so we're looking at minimum these are the the five number summary things that you'll find in box plot the minimum is equals min that's the length the minimum length is 17 percentile include formula that is we're looking at the 25th percentile and then the median equals median you could also use the same formula but instead of 0.25 make it 0.5 that gives you the same thing as median and i'm just going to cop this i'm going to copy this formula i'll paste it here you're doing the 75th percentile actually instead of 75th percentile you could just do 75 which is the same thing as 0.75 that gives you the 75th percentile maximum max and there you have it so now we have our box with box plot with whiskers for the length you have the the minimum the 25th percentile median 75th percentile and the max and if you want to make this really fast when we set these formulas up you'll notice that there are they're not anchored you put dollar sign in there if you want to anchor the row or the column these do not have that this basically says give me what's next to it minus the average of everything in that row in the column excuse me and this just looks at whatever the square root of the cell next to it so we can select these i'm going to copy these and you can paste them into here and you'll have the appropriate those you'll you'll have all of the the squares the square deviations in there computed for you and then let's see i'm going to just copy these and paste them over here and then we'll make some adjustments and we'll do the same thing over here i'm going to select these cells i'll copy them okay but and kind of cheated put an in here that'd make it easier and so we're looking at so the birth birth weight instead of let's put the mode will do the same thing sum of squares so where is that is it that's what we're looking at replace that with okay this is for instead of what am looking so put an down here because birth weight is in column yeah it's right here column so it makes it by having something like this set up when you copy the formulas there's relative thing in there so it only does relative to that distance when it's copying and so you have to update where you're doing these from that's just the square root of what's above okay so we have to do it down here too this should be so i'm going to do replace instead of column we'll make it column and because have bunch of cells selected control is find and replace it opens up this dialog box and because only have these specific cells selected they those that's only where it's going to be replacing if you don't have an array of cells selected it could replace everything in your table which is not exactly what you want but because that's selected it should be fine so you replace all made all done made five replacements and so now the box plot for birth weight looks like it should so let's look at this one we're going to take and replace it with with the control opens up the dialog box find the column replace it with column and that's how they're in excel all done we made 10 replacements plot looks okay let's start looking at the sum of squared it didn't like that instead of we want think let's see gestation is sum of squares it's okay we want because that's just the gestation period but we want the deviations okay now that thing looks like it should this one was already left in here and so that that gives us all the figures we have we have the mean mode sum of squared the sample variance the stand the sample standard deviation we have the five number summary of minimum 25th percentile median 70th percentile and maximum all populated in here but actually yeah and there i'll go ahead and this you