0@Loc: Person/c26.cha1@PID: 11312/t-00015820-12@Begin3@Languages: eng4@Participants: TS Teacher, SS Student5@ID: eng|Person|TS|||||Teacher|||6@ID: eng|Person|SS|||||Student|||7@Media: c26, video8@Comment: C-26 GRAPH; First 40 lines of text do not have9corresponding video10*SS: graphing, frequency distributions, histograms, and graphing means11[= reading from card].12*TS: ok, great.13*TS: ok, first I wanted to ask if you had any questions about anything14so we can emphasize that, if you do.15*SS: um, no I don't think so.16*TS: it was clear?17*SS: uh huh.18*TS: stuff you've been exposed to?19*SS: yeah, I had it in stats, but I had to go back and review the20standard deviation.21*TS: ok.22*TS: well tell me then what a population is.23*SS: a population, um, like a group of people, um, a group of subjects.24*TS: then what would a sample be?25*SS: a sample is like, let's see, you take a portion of the population26or a part of the population.27*TS: alright, so you do think it would be pretty safe to say that most28typical evaluations for research are done on samples rather then29populations?30*TS: ok, well what are some of the obvious reasons?31*SS: well, the population would be too big.32*TS: uh huh.33*SS: it would take too much time, it would be almost impossible to try34to use an entire population, whereas a sample &=mumbles.35*TS: &=mumbles ok, there are two main reasons for using the stats or two36uses for them and, you know, the use for it corresponds with the37meaning of it and so can you tell me what those are?38*SS: um, it's used to describe the population.39*TS: yeah, right or it describes the sample.40*SS: yeah, yeah.41*TS: and that would be called what kind of stats?42*SS: it would be descriptive.43*TS: yeah, sure.44*SS: and then inferential would be you use what you learn from the45sample to infer to the whole population.46*TS: right.47*TS: in other words it's important to remember that the results of an48experiment are based on data taken from a sample of the population.49▶50*TS: so, findings rarely come from a whole population, and sort of the51underlying motivation for most stats then is to first you describe52it, and then you have to determine how accurate a view of the53population it offers so that um &=mumbles. ▶54*TS: ok, um, the inferential then to kind of expand on what you said55allows you to decide if the experiment were conducted over and over56or if you were able to examine the entire population, how accurate57would your results be? ▶58*TS: how applicable to the real situation or to the whole population59would it be? ▶60*TS: ok, do you see how those are kind of interrelated? ▶61*SS: uh huh. ▶62*TS: in other words you use the descriptive statistics to sort of63describe your data, and it's also good for summarizing it rather64than looking at a bunch of raw data. ▶65*TS: if you can describe and summarize it, then you can you use your66inferential types of things to see how accurate that description is.67▶68*TS: ok, alright, um, what then is a frequency distribution? ▶69*SS: a frequency distribution is, you put like you list the scores in70the order like they, um, I think you list them from like the lowest;71you don't have to mess from lowest to highest. ▶72*SS: you just list the scores and then from that you can get the sum,73and you can get the sum of the means, and. ▶74*TS: ok, that's not exactly it. ▶75*TS: basically what a frequency distribution is, it's just a um, count76or a tally of how many scores or values at each type of point there77are. ▶78*SS: uh huh. ▶79*TS: in other words, you have your, they often refer to your dependent80measure and you have say if your dependent measure was on a scale of81one to ten increments, and it would be like how many people scored82one's? ▶83*TS: how many people scored two's, three's, four's, five's, and so on. ▶84*TS: so it's basically just a tally or a count of how many subjects85receive each possible score on a variable. ▶86*TS: ok, alright, um, what I'd like to do is sort of come up with a87hypothetical experiment so you can start looking at distributions88and things like that. ▶89*TS: so, let's just suppose for example that you were looking at, um, a90study in which you were trying to investigate the relationship of91empathy between the therapist and client, and how much better the92client gets. ▶93*TS: what is the client's outcome? ▶94*TS: and so it would be for our measures, we'd have the high empathy95group. ▶96*TS: that's our independent variable that's the manipulation, one group97that got high empathy from the therapist and one that got low. ▶98*TS: ok, so in other words you have two groups. ▶99%act: SS draws groups while speaking100*TS: x@l one, they get low empathy, and x@l two gets high. ▶101*TS: ok. ▶102*TS: alright, if we wanted to, let's say our measures, for our dependent103measure we ask the client to fill out a questionnaire. ▶104*TS: um, how much have you improved in therapy? ▶105*TS: and rate it on a one to ten scale. ▶106*TS: ok, so that's our dependent measure, and our independent measure107then is, Ok, what we manipulated. ▶108@Comment: pic001 (c26/image001.gif)109*TS: so if we wanted to do a frequency distribution [= draws axes]. ▶110*TS: for our scores, Ok, let's say in our low empathy group we had x@l111one equals low empathy, and in our high empathy group we got that112[= TD writes several illegible numbers on board to right of low empathy group and high empathy group].113▶114*TS: ok, how might we draw a frequency distribution of that? ▶115*SS: this would be the frequency [= t indicates Y axis]? ▶116*TS: sure. ▶117@Comment: pic003 (c26/image003.jpg)118*SS: 0 [= numbers Y axis]. ▶119*SS: and, um, would you put x@l one? ▶120*SS: 0 [= indicates x axis]. ▶121*TS: ok, what you usually want to look at in a frequency distribution is122usually the bottom referring to your measure. ▶123*SS: ok. ▶124*TS: so what you'd want to do is put each, yeah, empathy goes down. ▶125@Comment: pic005 (c26/image005.jpg)126*TS: there, one mark for each one down there. ▶127*TS: 0 [= refers to X axis]. ▶128*SS: 0 [= labels X axis empathy and 1-10]. ▶129*TS: ok, so now there's two ways that we could do this, or picture the130presentation. ▶131*TS: do you know what those are? ▶132*SS: a bar graph and a frequency. ▶133*TS: they call it a polygon. ▶134*SS: yeah. ▶135*TS: the frequency polygon or the bar graph. ▶136*TS: in other words the bar graph is. ▶137*SS: is a histogram. ▶138*TS: ok, great. ▶139*TS: let's start off then with the polygon. ▶140*SS: ok, three . ▶141*TS: how many three's do we have? ▶142*SS: one. ▶143%act: plots first point.144@Comment: pic007 (c26/image007.jpg)145*TS: let's do one variable at a time, Ok, so how many of this do you146have a five score for? ▶147*SS: one. ▶148@Comment: pic009 (c26/image009.jpg)149*SS: 0 [= plots next point]. ▶150*SS: seven. ▶151*TS: ok. ▶152@Comment: pic011 (c26/image011.jpg)153*SS: 0 [= plots one seven score]. ▶154*TS: ok, how would it change if we had two three's? ▶155*SS: it would be there156[= plots points above three score at a frequency of two]. ▶157@Comment: pic013 (c26/image013.jpg)158*TS: great, ok, now draw the line. ▶159@Comment: pic015 (c26/image015.jpg)160*TS: 0 [= connects the points]. ▶161*TS: ok, so there we have a dependent measure and we have an independent162measure. ▶163*TS: ok, let's look at the other one. ▶164*TS: umm. ▶165*SS: xxx [= while plotting frequency of high empathy scores]. ▶166*SS: 0 [= couldn't see points]. ▶167*TS: just do a dash or dotted line where they overlap. ▶168%act: draws in dashed line where overlaps169@Comment: pic017 (c26/image017.jpg)170*TS: ok, good. ▶171*TS: now, try it in a histogram form. ▶172*SS: do we just erase? ▶173*SS: 0 [= erases polygon]. ▶174*TS: ah, yeah that's fine. ▶175*TS: I'll go ahead and give you some more measures. ▶176*TS: let's say [= adds more illegible values]. ▶177*TS: go ahead and try that. ▶178@Comment: pic019 (c26/image019.jpg)179*TS: ok, two three's, it would be in the center with the bar over; Yeah.180%act: SD draws first bar181*TS: ok. ▶182%act: SS continues plotting183@Comment: pic021 (c26/image021.jpg)184*TS: if you want you could draw like two bars on there and make the185lines go different ways. ▶186*SS: like a solid bar and then a stripe. ▶187@Comment: pic023 (c26/image023.jpg)188*SS: 0 [= Continues plotting]. ▶189@Comment: pic025 (c26/image025.jpg)190*SS: 0191[= plots another bar on 5 and stripes one bar and colors another solid to show overlap between high and low empathy].192▶193*TS: ok, super. ▶194*TS: and that just gives you a kind of a way to compare what are the195most frequent scores you're getting. ▶196*TS: well looking at that it looks like possibly. ▶197*TS: xxx. ▶198*TS: ok, alright, just one last time from last week. ▶199*TS: the independent variable was the what from last week? ▶200*SS: the independent variable was how much the improved. ▶201*TS: ok, that was the dependent variable. ▶202*SS: ok. ▶203*TS: the one that you manipulate or change is a quick way to tell which204one. ▶205*TS: the dependent was the one with a score on the test. ▶206*SS: ok. ▶207*TS: ok, um (.) descriptive statistics then. ▶208*TS: we've talked about descriptive and inferential statistics. ▶209*TS: so descriptive statistics usually fall into two categories, Ok, do210you know what those categories are? ▶211*SS: ah, descriptive, um it would be (.) central tendency and &=mumbles.212▶213*TS: right, right, so what then is central tendency? ▶214*TS: what would that be? ▶215*SS: um, the central tendency is, I know it's the mode, the median, and216the mean. ▶217*TS: but what are they all kind of doing? ▶218*SS: ah, like telling you what the average score is, what the average219most score would be. ▶220*TS: average not as in the mean, but what is sort of the representative221score? ▶222*SS: which score appeared most, um, which score was the middle score. ▶223*TS: so in other words the central tendency sort of tells what the224sample as a whole is like, or it sort of representative of every225score. ▶226*TS: every score is figured in. ▶227*TS: ok, ah, so you just named the three types. ▶228*TS: xxx. ▶229*SS: ok, the mean you sum up the scores, like you'd say three plus three230plus five plus seven and you'd divide it by the number of scores231that you have. ▶232*TS: which would be. ▶233*SS: six. ▶234*TS: alright, and so it's just the average. ▶235*TS: what about the median? ▶236*SS: the median is like the number that has fifty percent of the scores237above it and fifty percent of the scores below it. ▶238*TS: ok, in other words if we had something that looked like this, where239would the median be? ▶240@Comment: pic027 (c26/image027.jpg)241*TS: 0 [= lists column of values]. ▶242*SS: it would be between five and seven. ▶243*TS: ok, alright, the mode, what is that? ▶244*SS: the mode is like the score that appears the most. ▶245*TS: ok, like we have here [= points to graph]. ▶246*SS: seven and nine. ▶247*TS: in other words, there's two modes. ▶248*SS: uh huh. ▶249*TS: so, it's possible that you have two modes &=mumbles. ▶250*TS: ok, so when might the median or mode be a better measure of central251tendency? ▶252*TS: I mean, usually when you think central tendency you think of the253mean but xxx. ▶254*SS: when there are extreme scores. ▶255*SS: the mean wouldn't take that into account. ▶256*SS: it would make it seem like the mean was more than it would be. ▶257*TS: let's say you had a plot that looked like this. ▶258*TS: 0 [= draws scatter plot]. ▶259@Comment: pic029 (c26/image029.jpg)260*TS: well, if you just had that &=points:a then a score would be more261representative, but then if you had a score up here &=points:b when262it was actually down here &=points:a. ▶263*TS: ok, the book, used the example on page one hundred and thirty264three. ▶265*TS: it said it could look like, you know it said if you had a266relatively few number of individuals with a high income, it could267look like the whole county had a whole lot more income. ▶268*TS: the average person had more income than was actually the case. ▶269*TS: ok, um, Ok, what then if you wanted to draw some of these, what270would a distribution like say our bimodal distribution look like? ▶271*SS: um, bimodal. ▶272*TS: bimodal distribution. ▶273@Comment: pic031 (c26/image031.jpg)274*TS: since the mode is the most frequently occurring score it would be275that &=points:a. ▶276*TS: 0 [= puts graph on board]. ▶277*TS: ok, alright. ▶278*TS: what do you think of this one? ▶279*TS: do you remember what the normal distribution looks like? ▶280*SS: it's just a bell shaped. ▶281*TS: bell shaped curve. ▶282@Comment: pic033 (c26/image033.jpg)283*TS: 0 [= Draws curve]. ▶284*TS: ok, so where would the mode be on that? ▶285*SS: the top. ▶286%act: TS puts point on top287@Comment: pic035 (c26/image035.jpg)288*SS: the median? ▶289*TS: in the center. ▶290*SS: 0 [= draws line down center]. ▶291@Comment: pic037 (c26/image037.jpg)292*TS: the mean? ▶293*SS: it would be like the score in between, like the center about. ▶294*TS: the mean would be the same thing. ▶295@Comment: pic039 (c26/image039.jpg)296*TS: 0 [= highlights over center line]. ▶297*SS: ok. ▶298*TS: by definition, a normal distribution is one in which the mean,299median, and the mode are all the same. ▶300@Comment: pic041 (c26/image041.jpg)301*TS: that's what makes it normal. ▶302*TS: but like if you, on our bimodal distribution that we had drawn a303second ago. ▶304*TS: 0 [= Draws bimodal curve]. ▶305*TS: ok, here were our modes, here the mean and median were here. ▶306@Comment: pic043 (c26/image043.jpg)307*TS: 0 [= Indicates two modes (a) and mean/median (b)]. ▶308*TS: but with a normal, they're all the same. ▶309@Comment: pic045 (c26/image045.jpg)310*TS: and of course it's possible to have a distribution where they're311all different. ▶312*TS: 0 [= draws distribution]. ▶313*TS: in other words in a skewed distribution the mode would be where? ▶314*SS: the top again &=points:a. ▶315*TS: sure, and then the median part would be about here &=points:b since316you've got the scores tagging on out here. ▶317*TS: and the mean would be around in here &=points:x. ▶318*TS: so it's possible to have them all different xxx. ▶319*TS: ok, ah, we've covered central tendency and what is the difference320between the mean, median, and mode. ▶321*TS: so what is our other. ▶322*SS: variability. ▶323*TS: variability, and what is that? ▶324*SS: um, it's like the standard deviation. ▶325*SS: like how variable the numbers are. ▶326*SS: um, I don't know what I'm trying to say. ▶327*SS: I know it's like the standard deviation, how variable the numbers328are. ▶329*TS: well, let's think about it a minute. ▶330*TS: if it's variability that means the numbers vary. ▶331*SS: yeah, how the numbers vary, how the scores vary. ▶332*TS: so what might be another word for that? ▶333*SS: (.) how they deviate? ▶334*TS: ok, deviate or different xxx. ▶335*SS: um, the standard deviation is like the standard, um, deviation of336the scores around the mean? ▶337*TS: uh huh. ▶338*SS: and, um, the formula xxx. ▶339*TS: see if you can tell me. ▶340*TS: basically in words, the standard deviation indicates the average341deviation of scores around the mean. ▶342*TS: so what then is the variance, or how is it related to the standard343deviation? ▶344*SS: well, I know like variance you take the square root of it to get345the standard deviation. ▶346*TS: right, and so the standard deviation, Ok, the variance is the sum347of the squared deviations, and the standard deviation which is the348square root of that sort of indicates the average deviations. ▶349*TS: it's kind of looking at the xxx average distance. ▶350*TS: it takes into account each of the single raw score's deviation from351the mean and averages them and comes up with a score such that on352average that's how much a score varies above or below the mean that353much. ▶354*TS: alright, for example, a standard deviation of two point thirty six355means that subject's scores lie two thirty six units either above or356below the mean. ▶357*TS: so that leaves one more measure of variability that the book talked358about. ▶359*TS: do you remember? ▶360*TS: the extremes, the range. ▶361*SS: oh, yeah. ▶362*SS: I remember. ▶363*TS: what is the range? ▶364*SS: it's like, um, when the scores fall within a range of numbers like365from the highest to the lowest. ▶366*TS: sure, it's just the difference between the highest score and the367lowest scores. ▶368*TS: xxx ok, alright so we graphed some frequency distributions, and we369got our dependent measure and we looked at how many times each value370or level of that dependent measure occurs. ▶371*TS: so in a frequency distribution you're kind of just looking at the372raw scores. ▶373*TS: but you can also graph means. ▶374*TS: why do you think we would want to do that? ▶375*SS: um, to graph means? ▶376*SS: it would probably, it would make it easier to see, I mean usually377in a distribution there would be a large amount of numbers. ▶378*SS: the mean would like narrow it down. ▶379*TS: in other words the mean would make it a lot easier to look at, well380it would do a lot of things. ▶381*SS: yeah. ▶382*TS: first of all, literally and simplistically it would make it easier383to draw. ▶384*TS: second, it would make it easier for a person looking at it to385understand because you wouldn't see a bunch of dots. ▶386*TS: it's kind of easy to get lost xxx so to speak. ▶387*TS: and then thirdly and related to that it kind of summarizes the388data, and since our measures of central tendency such as the mean389does what? ▶390*TS: summarizes or represents a whole distribution then it's just a391short hand way of looking at the whole thing. ▶392*TS: so in other words, in a sense it gives you a sort of essence of all393the scores but in a condensed fashion. ▶394*TS: ok, so it looks like our mean is about six point five395approximately. ▶396*TS: maybe seven [= indicates data from first graph]. ▶397*TS: so, if you wanted to calculate it you'd add up the scores and398divide by six, right? ▶399*SS: uh huh. ▶400*TS: let's say the approximate mean is equal seven, that's just our401guess. ▶402*TS: up here it looks like about five maybe a little more than five403maybe because we got three sevens and only two threes xxx. ▶404*TS: how could we go about graphing these means? ▶405*SS: would you do it kinda the same way as you did. ▶406*TS: ok, first of all look at it. ▶407*TS: your independent variable again is. ▶408*SS: empathy. ▶409*TS: ok, and it needs to go on which axis? ▶410%act: SS labels axis411@Comment: pic047 (c26/image047.jpg)412*SS: this one. ▶413*TS: that leaves what, the X axis? ▶414*SS: xxx. ▶415*TS: well, no, the score values. ▶416@Comment: pic049 (c26/image049.jpg)417*TS: the scores are how much they improved. ▶418%act: SS puts values on Y axis419*TS: it's scores on this test but what it's theoretically tapping is420client outcome or improvement. ▶421@Comment: pic051 (c26/image051.jpg)422*TS: so we've got client outcome as our dependent measure and empathy as423our independent measure. ▶424*TS: so, we need to draw little lines or graduations. ▶425*TS: well, we only had two, high and low. ▶426%act: SS adds lines to X axis427*TS: xxx then you need to put graduations for the scores. ▶428@Comment: pic053 (c26/image053.jpg)429*TS: ok, alright. ▶430*TS: so we're guessing our approximate mean for our low empathy group431is. ▶432*SS: seven? ▶433*TS: that's not right. ▶434*TS: our data is not supporting our hypothesis (.) x@l one is seven. ▶435*SS: ok. ▶436*TS: 0 [= plots first point]. ▶437@Comment: pic055 (c26/image055.jpg)438*SS: and x@l two is, now wait that's right. ▶439*SS: where did I get three? ▶440*SS: that should be a five. ▶441*SS: so x@l two is seven! ▶442*TS: seven would be the high empathy. ▶443%act: SS erases first point444*TS: you got to call me on these things. ▶445@Comment: pic057 (c26/image057.jpg)446*TS: and that would be a five instead of a three. ▶447%act: SS plots X2 point as 7 and X1 point as 5.448*TS: let me get my head cleared. ▶449*TS: so we've got x@l two our high empathy is a seven, and x@l one our450low empathy is a five. ▶451@Comment: pic059 (c26/image059.jpg)452*TS: if you wanted to do it in the line graph form you need to draw a453line. ▶454%act: SS connects points455*TS: and if you wanted to do it in bar graph that would be what. ▶456*SS: 0 [= adds bars]. ▶457@Comment: pic061 (c26/image061.jpg)458*TS: so, we graphed the means. ▶459*TS: and you can see in our frequency bar graph460[= Indicates first graph] and sure that gives us some information461but this tells you a little bit easier in terms of what the462relationship is as far as it looks like the higher the empathy the463better the outcome as defined, operationally defined by the score on464our test. ▶465*TS: alright, did you pay any attention to what was going on on page one466hundred and thirty four what they did to make the data look467different? ▶468*TS: turn to that for a second. ▶469%act: SS turns to page 134470*TS: can you see how both of those are, neither one is actually a lie or471not accurate? ▶472*TS: but do you see what they've done? ▶473*TS: they made the increments a lot different such that it looks a lot474more dramatic. ▶475*SS: uh huh. ▶476*TS: and there's other ways of doing that too such that the data look477more dramatic with graphing. ▶478*TS: in other words, using their cola as an example. ▶479*TS: if you had cola a and cola b and the percent, forty percent chose480cola a and thirty five chose cola b@l. ▶481@Comment: pic063 (c26/image063.jpg)482*TS: ok, that's one way to look at that. ▶483%act: draws graph while speaking484*TS: another way to make it look more dramatic would be to top the485scale. ▶486@Comment: pic065 (c26/image065.jpg)487*TS: it's the same size increment but just showing the top increment. ▶488%act: draws while speaking489*TS: or you can do something really dramatic like they did in the book,490and change the size of the increments. ▶491@Comment: pic067 (c26/image067.jpg)492*TS: if you wanted to make this increment by ones. ▶493%act: plots graph494*TS: cola a is way up here, everybody is drinking it, and poor cola b is495down here. ▶496*TS: so any way, the reason you want to keep this in mind is so you'll497know that the graphs are not inaccurate, but that there are dramatic498and less dramatic ways to show the results. ▶499*SS: uh huh. ▶500*TS: so, just to review then. ▶501*TS: what are samples and populations? ▶502*SS: um, population is like the whole or entire group and a sample is a503portion of that. ▶504*TS: ok, in other words subjects scores have some kind of common505characteristic and the sample is a subgroup of that population. ▶506*TS: ok, and two reasons for usig the two types of stats would be? ▶507*SS: um, two reasons would be to describe and to infer. ▶508*SS: to describe would be descriptive and inferential would be where you509gather ideas from the sample and you infer it to the population. ▶510*TS: in other words you use your descriptive to describe what happened511to your sample, and then you can use your inferential to decide how512applicable those findings are. ▶513*TS: how certain are you? ▶514*TS: how well does it apply to the population and how certain you are515that it applies that way. ▶516*TS: ok, um, so it's important for you to know that the results of an517experiment are seldom if rarely based on the whole population and518the best you can do is a probabalistic way. ▶519*TS: ok, um &=mumbles. ▶520*TS: a frequency distribution then is what? ▶521*SS: um, like the scores put down. ▶522*SS: the independent variable is on one line and the scores on the523other. ▶524*SS: the frequency of the times they occur, you graph those. ▶525*TS: you usually look at your dependent measure. ▶526*SS: yeah, dependent. ▶527*TS: you put your dependent measure down here528[= Indicates x axis of graph on board] and then look at the number529of times at your independent measure that each occur. ▶530*TS: ok, so it's a count or a tally of how many times, the occurrences531that you had at each level of your variable. ▶532*TS: ok, um, and the frequency distribution can then be presented533pictorially in different ways which are. ▶534*SS: um, a histogram [= the bar] and, um, a polygram. ▶535*TS: a polygon. ▶536*TS: similar to the line graph. ▶537*TS: ok, and, um, descriptive statistics then looking at those in538particular fall into two main types of categories that were laid out539in the book which are. ▶540*SS: um (.) it would be, um, central tendency and variability. ▶541*TS: ok, so, in other words, descriptive statistics usually looks at542those two different things. ▶543*TS: how much they vary, sort of, and in a sense how much they're544staying the same, but, what is sort of representative about xxx. ▶545*TS: ok, so the variability looks at the difference, the discrepancy,546how they differ from each other, and then central tendency tries to547represent the group as a score. ▶548*TS: ok, and so the three measures of central tendency you usually think549about are? ▶550*SS: the mode, the mean, and the median. ▶551*TS: which are? ▶552*SS: each one of 'em? ▶553*TS: uh huh. ▶554*SS: the mode, the mode is more like the score that occurs the most. ▶555*TS: uh huh. ▶556*SS: and, ah, the median is the number if you count from the center the557number that fifty percent is above and fifty percent is below. ▶558*TS: uh huh. ▶559*SS: and the mean is just the sum of the numbers, or the scores divided560by the total number of scores. ▶561*TS: the average. ▶562*SS: yeah, the average. ▶563*TS: and you notice how in a distribution it's pretty easy to pick out564the mode just by looking at which one occurs the most, but when you565graph the means then you get a lot more information. ▶566*TS: ok, first of all what is the variability then, what does that look567at? ▶568*SS: how they differ. ▶569*TS: from each other, sort of the spread. ▶570*SS: uh huh. ▶571*TS: of the distribution. ▶572*TS: ok, really technical terms but it's the extent to which the scores573differ from their central tendency. ▶574*TS: ok, so the standard deviation and variance are two sort of related575scores, types of measures of variability, and what do they refer to?576▶577*SS: variance is like the average, um, average deviation scores around578the mean, and then the standard deviation is the square of that. ▶579*TS: in other words the variance refers to the sum of the squared580deviations as far as the mean, whereas the standard deviation sort581of indicates the average deviation, and they're related because like582you said the variance is the standard deviation squared. ▶583*TS: ok, and that leaves the range which is? ▶584*SS: um, the spread of the numbers, it's like the highest number minus585the lowest number. ▶586*TS: yeah, Ok. ▶587*TS: in other words the difference between the highest and the lowest588score. ▶589*TS: and, then, Ok, so you've got all that, but then a good way to590summarize and make your data much more readable and much easier to591deal with; I mean, in other words, the mean is a measure of central592tendency which is representative of your group any way, and then by593graphing it you can sort of look at the relationship between the594two. ▶595*TS: ok, so there's two ways to graph that which would be your. ▶596*SS: bar graph, and line graph. ▶597*TS: ok, and we went through that. ▶598*TS: um, now did you have any questions, or is all clear? ▶599*SS: no. ▶600*TS: ok, well you said you had somewhere to go so I'll cut you loose. ▶601@End