For more information, please see full course syllabus of Statistics

For more information, please see full course syllabus of Statistics

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### Dotplots and Histograms in Excel

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Roadmap 0:06
- Roadmap
- Previously 1:02
- Data, Frequency Table, and visualization
- Dotplots 1:22
- Dotplots Excel Example
- Dotplots: Pros and Cons 7:22
- Pros and Cons of Dotplots
- Dotplots Excel Example Cont.
- Histograms 12:47
- Histograms Overview
- Example of Histograms
- Histograms: Pros and Cons 31:39
- Pros
- Cons
- Frequency vs. Relative Frequency 32:53
- Frequency
- Relative Frequency
- Example 1: Dotplots vs. Histograms 34:36
- Example 2: Age of Pennies Dotplot 36:21
- Example 3: Histogram of Mammal Speeds 38:27
- Example 4: Histogram of Life Expectancy 40:30

### General Statistics Online Course

### Transcription: Dotplots and Histograms in Excel

*Hi and welcome back to www.educator.com.*0000

*We are going to be talking about dot plots, and histograms in Excel today.*0003

*First we are going to talk about going from data to dot plots.*0009

*Remember before we always have to go from data to frequency tables and then to some visualization.*0013

*Dot plots are nice because they can let you go straight from data directly to the visualization.*0019

*We are going to talk about going from data to histograms.*0024

*Histograms are going to be really helpful to us especially because a lot of times we are going to have variables that have many values.*0028

*We are going to talk about how do we have grouped, ungrouped values, which we have looked up before, and grouped values.*0039

*Finally we are just going to talk a little bit about plotting frequencies versus relative frequency.*0046

*Relative frequency is just a fancy way of saying it is frequency but divided by how many cases you have.*0052

*It is really like percentage.*0060

*Previously we always have to go from data and we had to stop over at making a frequency table and then go to the visualization.*0065

*But now with dot plots we cut out the middleman and we can go directly from data to the visualization.*0073

*That is a really handy thing there.*0079

*If you look in your Excel file the data is going to be the same as the data we have been working with, the 100 www.facebook.com friends.*0085

*Here is what we are going to do, before we had created a nice little graph*0094

*using the Excel tools to create visualization but now we are going to use dot plots.*0100

*Excel will create dot plots for you directly.*0108

*Instead we have to sort of fidget, the fudge actually comes in handy sometimes.*0111

*Let us go birth month.*0119

*We already know that birth month should have a uniform distribution.*0121

*We already looked at this data before.*0125

*What we are going to do is just look at how to transform it directly*0127

*from data into a visualization without having to use the Excel graphs or chart.*0131

*If you go to your birth month sheet here I have just put up the months, 1 through 12.*0140

*It just looks sort of like a frequency table but if you watch carefully we are going to transform it.*0148

*Let us go ahead and put in our regular formula for how to find frequency.*0156

*That is equal sign (=) because we are starting off with a function.*0163

*Count if because we wanted to count if that person was born in the month of January.*0167

*Let us put in our data.*0177

*If we click on data and we scroll down to months, here is birth month.*0180

*I'm going to select all of these rows.*0188

*So far it seems like we are just making a frequency table.*0192

*I’m going to put in a comma because I know I’m going to need that.*0197

*Let us go back to birth month.*0201

*I want you to count it if the birth month is January.*0203

*If we just hit enter here, that would mean we are just counting how many people are born in January.*0210

*We are going to do something a little bit different.*0217

*I want Excel to visualize for me how many people there are.*0219

*Not give me a number but actually show me a pictures.*0224

*Here is what we are going to use.*0229

*We are going to use the repetition function and so that is rept, you do not have to put it in capital.*0230

*I just wanted to distinguish it from the count if and put a parentheses because that is how you are going to put in the inputs.*0238

*Here Excel reminds us that we need text, whatever text you want to repeat over and over again and the number of times.*0247

*The text, you can pick your favorite text.*0256

*You just have to make sure that it is in quotation marks.*0259

*I'm going to put in an at symbol, that is my favorite one.*0263

*I’m going to close parentheses and put in a comma.*0271

*The beautiful thing about count if is that it is going to return to me a number.*0274

*The output is going to be a number.*0279

*If I just leave this here it will just output to me 7.*0282

*This function will actually read repeat this at symbol 7 times.*0287

*At the end of this I’m going to put a close parentheses.*0296

*That my parentheses match up.*0302

*And then I’m going to hit enter.*0305

*Great.*0308

*Let me just make these rows a little bit larger so you can see everything.*0311

*Here instead of having the number 7, I have 7 little symbols.*0317

*And you do not have to use the at sign (@) if you do not want to.*0323

*You could use a star, an asterisk.*0327

*You could use anything you want.*0332

*You could use an o, anything to help you see there is this many people born in the month of January.*0333

*This is a direct way of going into the visualization.*0347

*We can actually copy and paste this just like we did before.*0351

*All we have to do is make sure that our data is locked with our dollar signs.*0357

*I’m going to hit enter and all I’m going to do is take that, drag it all the way down and we have a visualization right there.*0367

*We do not have to make Excel do any extra work with the charts or anything like that.*0377

*That is the handy thing about a dot plot.*0382

*We are making dot plot in Excel but a lot of times you may be asked to make dot plots on paper and pen.*0385

*No actual statistician does that anymore but in a statistics class you maybe asked to do that.*0392

*The nice thing about dot plots is that you do not have to put the data in order or anything.*0399

*You could just go and just sort of go down the line and put a dot where 5 is,*0404

*put a dot where 3 is, put a dot where 6 is, put a dot where 9 is.*0412

*You can see that it is a really easy way to visualize the distribution and you do not have to do anything to your data before hand.*0416

*But once again doing it by hand pretty tedious and people do not really do it that way.*0426

*At least not when they are doing real statistics.*0431

*Alright, that is dot plots but let us talk about the pros and cons.*0435

*Dots plots, the pros and cons.*0445

*The pro is that it is nice and quick.*0447

*It is quick and dirty, right.*0451

*You could go directly from data to dot plots, no middleman, no frequency tables.*0453

*You do not have to know anything even about statistics and you could do it.*0458

*You can only do this with small data sets.*0461

*It is not useful with giant data sets.*0465

*Even your data set of a 100 cases, it is considered a relatively small data set.*0467

*Imagine if you have like a thousand of cases, I mean just to even see your dots go all the way to the side.*0473

*I mean it is going to be pretty crazy, right?*0481

*That is sort of a pro and a con, when you have a small data set this is a really nice thing to do.*0485

*Con is it cannot handle a lot of data points.*0494

*Another pro is that it shows the actual individual values so*0499

*you will know exactly what each dots stands for and it does in group cases together.*0503

*Everything sort of spread out for you and it shows you the shape of the distribution.*0509

*With our example we saw once again that it is a uniform distribution and you could see that right away.*0514

*The cons is sort of the opposite but it is really the same features as the pros but considering it from a different goal perspective.*0521

*One of the pros is that you can handle small data sets really well but the con is that it cannot handle a lot of data points.*0533

*The other con is that because it shows these individual values, it cannot group the cases together.*0540

*I forgot to show you one thing.*0549

*If you go back to the birth month sheet, one thing is this is a vertical*0551

*or horizontal but here each row represents one of the values of this variable.*0563

*Now sometimes you may be asked to create a dot plot where the dots are going up and down.*0571

*I will call that vertical version.*0580

*It is really easy to make that once you have created this.*0582

*Here is how to do it and this is a nice trick.*0584

*It is just something nice to know with Excel as well.*0590

*If you copy this, I'm using command C here and I'm just going to paste it over here on this side.*0595

*I guess I will paste it here for now.*0605

*We are going to have to change this, I will paste this down here so that you could see it is going up.*0609

*Here is what I’m going to do, I’m going to paste it special.*0616

*If you go to add it, you should be able to see something that says paste special.*0621

*Not a lot of people use this but if you click on paste special something like this will come out.*0633

*What I want Excel to do is transpose it, what is used to be columns, I want it to put it in rows.*0639

*I’m going to hit transpose.*0645

*It is just to paste it but it is going transpose paste it.*0649

*I will hit okay.*0653

*Here what we find is that it has put all of my rows into columns and columns into rows.*0656

*What I’m going to do is take these months here and*0664

*I’m going to cut them command x and I’m going to paste them below my frequency command v.*0672

*I’m going to select these dots from my dot plot and*0681

*then I’m going to use my formatting palette to tell it to face it in a vertical matter rather than horizontal.*0684

*Let us look at what this looks like.*0698

*I’m going to take this row and make it a little bigger so you could see.*0701

*I’m going to take all of these and shrink my column a little bit so you could see it all at the same time.*0713

*Hopefully you are able to follow along with that,*0722

*You will see that what I have done is I have taken my previously horizontal dots and I have made my dots vertical.*0725

*It is just formatting.*0734

*It is nothing special.*0735

*Honestly you could also do this from the very beginning if you know that is the way you need to do your dot plot.*0737

*Basically the information is the same though, that you could see that it is a roughly uniformed distribution.*0743

*There is not one month that is particularly popular.*0751

*They are just seem to be repeating pattern.*0754

*That is transposing dot plots.*0758

*Let us go on.*0766

*Let us go on to histograms.*0769

*Histograms will probably be the most frequent frequency distribution you use in your statistics course and in statistics real life.*0771

*Histograms are pretty easy to understand.*0780

*All you have to do is imagine drawing a rectangle around the dots*0783

*so that you do not see individual dots anymore but you will see rectangles.*0787

*What is nice about histograms is that you could group cases into bins.*0793

*For an instance, we could put everybody who is born in the winter months together into one rectangle.*0798

*We can have December, January, February, in one rectangle and then we could bin other months into another rectangle.*0806

*This is going to be useful to us when we have variables that have a lot of values.*0818

*For instance, take the example of variable like friends.*0824

*Friends is going to be an interesting variable to look at.*0828

*To look at what is the distribution of friends like in our www.facebook.com sample but people can have 1 friend.*0831

*People can have 15 friends, people can have 500 friends or 600 friends or 1000 friends.*0838

*The question is are we going to have a column for 1, 2, 3, 4, 5, all the way up to 1000?*0847

*That seems pretty crazy, right?*0857

*If we had an ungrouped frequency table it would look insane.*0859

*We probably have from like 1 all the way up to, let us be conservative and say 500.*0864

*We have one all the way up to 500 and then maybe we have one person that has 1*0879

*and then another person that has 3 and a couple people that have 10, 12 and 15.*0884

*Probably not one particular value of friends like 273 is going to be that popular, right.*0890

*It will be like everybody just has 1 person in there mean, right?*0897

*Every value would not have very many cases.*0902

*An ungrouped frequency table would be unhelpful to us.*0905

*In this case we want to use a grouped frequency table.*0912

*We probably want a mean of everybody who has from 0 to 100 friends together and then from 101 to 200 friends together.*0915

*And from 201 to 300 friends together something like that.*0924

*That will probably be a lot more useful for us.*0927

*Let us go back to our examples in the Excel file and let us go friends.*0929

*In friends I have prepared what looks like a regular frequency table so far.*0940

*It has frequency here, but here I have min of mean.*0946

*My minimum value of the mean and my maximum value of the mean.*0951

*For instance, if I want my bin to go from 0 to 100 then I would put in frequency all the people who are in between 0 to 100.*0955

*In order to establish the mean size that you want, one thing that is helpful to know in advance*0969

*is what is the minimum value in your data set?*0974

*And what is the maximum value in your data set?*0979

*Here I'm going to be using Excel functions to help me do that.*0982

*The Excel function is pretty easy to remember because it is just mean, in order to find the minimum value.*0988

*I will put in mean and I put in my parentheses and I'm going to make data.*0994

*I'm going to my friends variable.*1001

*See we have people who have like thousands of friends, 700 friends.*1005

*I'm going to close my parentheses there.*1024

*Here this is just saying look at all of this data and find the minimum value.*1027

*It turns out that somebody in our data set has 0 friends, it is sad for that person but cest la vie, life is okay.*1035

*It will go on even if you do not have any www.facebook.com friends.*1043

*Let us look at the maximum value.*1047

*The maximum value is pretty easy because it is just max and parentheses and putting in that same data.*1049

*Obviously you could also copy and paste.*1066

*I have put in a close parentheses and I just hit enter.*1069

*And I see that somebody in our data set has over 2000 friends.*1072

*Can you imagine having an ungrouped frequency table where you have to number from 0 to 2257?*1078

*And then look at every single value in between?*1085

*I mean a lot of them will probably be 0 and even a really frequent one will only be like 2.*1088

*This is a pretty useless link to look at in an ungrouped way.*1094

*That is why we want to look at it in a grouped histogram.*1098

*What kind of mean size would you like?*1102

*Maybe 100 but instead of 100 I’m going to put in 99 because it is going to be the formula that I'm going to create.*1105

*You could like to subtract one later but I am going to make it inclusive, I will explain it in just a second.*1116

*I'm lazy and I do not want to type in like 100 and 200, and 201 to 300.*1123

*I’m just going to use Excel functions in order to help me do that.*1130

*Now I know that my max bin here is from 0.*1135

*My first bin is from 0 to 100.*1139

*My next bin obviously is going to start where this bin leaves off.*1141

*I’m going to take my max of bin number and then just add 1, for now I have 101.*1146

*And because it is starting from 1 already I know that if I added 100 it would be 201 and then the next one will start at 202.*1155

*That is when start I made my been size 99 because I know it already starts off at 101 and that way I can make it nice and even.*1162

*When I tell my max been to be this thing, my mean of bin size plus bin size, then will get to 200.*1175

*Sometimes it may require little bit of playing around with the formulas.*1187

*You might have to add 1 or subtract 1 or something here.*1192

*I’m sure you can figure it out as you go.*1194

*I’m just going to copy and paste this all the way down.*1199

*I know what I forgot, I’m just going to undo that.*1204

*What I now is that this cell, I do not want it to ever change.*1209

*I want this to be locked in.*1214

*What I'm going to do is take that now it should be locked in and then copy and paste it.*1221

*A few paces down and then you can see it goes from 101 to 200, 201 to 300.*1230

*I’m going to go all the way up until I capture 2257, at least up to 2300.*1236

*That is like twice as much.*1246

*That is pretty good.*1253

*I have all my bins and even though I have how many rows, I have 23 rows but that is a lot fewer than having 2200 rows.*1255

*That is why grouped bins are better.*1270

*Now let us put in a range.*1274

*The range is just telling me what is my mean bin size and what is my max bin size*1276

*This is just to help me so that when I graph it, when I make a chart out of it*1282

*That this range will help us put something on the X axis that is really useful for us.*1288

*Let me put in a range and basically I'm going to make my range out of the mean of bin and the max of bin.*1295

*These two boarders and I’m just going to put a dash in the middle.*1302

*The way to do that is by using the concatenate function.*1306

*Concatenate just means to put things together.*1309

*I'm putting in an equal sign (=) and the word concatenate.*1313

*And I will put in a parentheses and I’m going to put in this value, that is my first text and a comma (,)*1320

*to separate my text but then whatever is in this Excel will just concatenate it together, put it all together.*1331

*And then I want to put in it a dash (-) and then I want to put it in my max order*1339

*and enclose that parentheses and let us see what happens.*1347

*Now I will get 0 to 100 and this is going to be helpful for us later when we want to label our X axis in a useful way.*1352

*Now that we have that, what we are going to ask Excel to do is find me the count of all*1363

*the people who have a friends counts between 0 and 100.*1374

*Before we have only learned how to count if it is one particular value.*1379

*How do I tell Excel count if it if it is within a certain range?*1385

*We are going to use what we call count ifs, it is not just count if it is count ifs*1391

*because we are going to ask Excel find everybody above 0 but also under 100.*1397

*I’m going to put equal sign (=) and put in count ifs.*1406

*Whenever I put in count ifs, I treat almost like it is two separate count is statements that I have just put into one set of parentheses.*1414

*I will put in the range for the first one and then the criteria.*1423

*I will put in the range for the second thing and then put in the criteria.*1427

*Here is what I mean, my range is going to be my friends data and I will put in a comma there*1431

*and here I know that this data is not going to change.*1451

*I’m going to lock it in place.*1454

*It is already been locked in, I’m going to delete this part for now.*1461

*We want to tell it do not just count it if it is equal to 0 but count it if they have a friend count that is greater than 0.*1467

*How do I do that?*1478

*I use my quotation marks, see if you could see that.*1479

*I use my quotation marks and I will tell Excel count it if their friend value is greater than or equal to,*1486

*and I’m going to close my parentheses because what I want to say is count it if it is greater than or equal to whatever is in here.*1496

*For Excel to know that you want to treat this is a number you want to put in a and symbol and then you want to click on that bin.*1505

*It is going to be counting everybody who has a friend count greater than 0 but that is everybody in your data set.*1518

*That is not what you want.*1525

*You also at the same time want Excel to tell you if the friend count is under 100.*1527

*I’m going to put in a comma and now we need to put in my criteria range number 2 and my criteria number 2.*1537

*I know that my criteria range is actually the same as this.*1544

*I’m just going to copy and paste this.*1548

*I’m using command c and I’m putting it here, command b so that now I just have that same range that is never going to change.*1550

*I'm going to tell Excel now tell me if these values are less than or equal to the max of bin.*1565

*The so less than or equal to, close the quotation marks.*1574

*Put in my and symbol and click on that.*1581

*It looks a little crazy but it just means count it if it is greater than 0 or less than 100 and then I'm going to close that.*1586

*And I find out we have 8 people will fit that profile.*1597

*The beautiful thing about Excel is that although it is hard to do that one cell it is like it is pretty complicated,*1602

*once you put in your dollar signs and lock everything in place that needs to be locked in place,*1609

*you could just drag that all the way down and you will get this beautiful frequency table that is been bins for you.*1615

*And now that you have this what I would do is select both the range and frequency, hit charts and hit XY scatter.*1624

*This is what sort of your frequency table looks like but let us put it into columns so that the range will show up well.*1641

*I’m just going to cover all my frequency table stuff, so you could see this a little bit better.*1653

*Now you will see that our histogram has the whole range from 0 all the way to 2300 and it is binned all my people together.*1659

*Its binned people who have 0, 1, 2, 3, 4, 5, 99 friends all the way into one bin.*1674

*In histograms, one thing you will learn is that because this axis is continuous you want your histogram*1684

*to also reflect that you have not skipped any values down here.*1691

*What you want to do is double-click on your on your bars and a format data series should pop-up.*1696

*What you are going to do is click on options and I’m going to tell Excel do not put any gaps in between my bars.*1712

*In this way histograms tell you there are no values that are skipped along here, every value has been accounted for.*1722

*That is our first binned histogram.*1733

*Obviously you could change your bin size and we are going to do that just that you could see.*1737

*I’m going to make this real tiny and leave it over here and we are going to do another example where we are going to change the bin size.*1744

*Maybe instead of 100, we will want a really big bins like 250.*1754

*Maybe instead of 100 and then I want may bin size to be to 250.*1768

*Because of that I should change this to 249 and all the work has basically been done for us already because we put in those formulas.*1777

*Let us see, I only needed to go up to 2257, 2500 is the earliest I can close it off.*1790

*I’m just going to delete these rows, they are not useful to me.*1804

*Let me delete all of these guys.*1815

*Let us look at our bins, I’m just going to make this histogram large and so we could see wow like Excel*1828

*has already done all the work for us, making the graphs and everything.*1837

*All we had to do is change a few numbers here and there and we see that we basically have that same distribution.*1840

*Remember this distribution is called a skewed distribution and we have this tail that goes out to the right side where the values get larger.*1847

*That is what we call a skewed right table and that is because we have a couple of people*1858

*who have an inordinately large number of friends but most people are between 0 and 500 friends.*1864

*www.facebook.com actually says that their average number of friends is 130 or something like that*1873

*which is pretty low in consideration with our data set where it seems like a lot of people have even 250 to 500 friends.*1879

*And so now let us go back to our slides.*1893

*I so that was the grouped frequency table.*1896

*Let us look at histograms, pros and cons.*1902

*The pros side when you have a large number of values to plot just like with things like friends*1904

*that is certainly a variable where you have a large number of values.*1912

*There are also things like a number of tagged photos, that is going to be a large number of values.*1916

*Some people have just a few photos.*1924

*Some people have a ton of photos right?*1926

*These kind of variables have a large number of values to plot and in that case a histogram is really nice particularly a grouped histogram.*1927

*Also a histogram is dead if you do not need to see individual values*1937

*and a histogram will definitely show you the general shape of the distribution.*1943

*For example in the case of friends we see that it is a right skewed distribution.*1947

*One con though is that if you have many distributions that you want to compare simultaneously, histograms are going to be a little bit hard to do.*1953

*You can probably compare up to two separate distributions on one histogram*1961

*and see how the distribution flow but more than to it gets a little bit clunky.*1966

*Let us talk a little bit about frequency versus relative frequency.*1975

*Frequency is simply how many cases have a particular value so how many people have between 0 and 100 friends.*1980

*Well maybe it is something like 250 people.*1991

*How many cases have a particular value between 101 and 200.*1998

*Well maybe that is 240 people.*2009

*This is basically what frequency looks like, it is just counting.*2014

*Now relative frequency is what proportion of cases from the sample have that particular value.*2018

*If you had 250 people having friends between 0 and 100 friends, what is that in relation to your entire sample?*2023

*Well if your sample, if your (n) is 1000 people in your sample then it would be 25% or .25.*2038

*And then between 101 and 200 instead of being 240 people it would be 24% or .24.*2054

*A pretty simple idea but it will come up again in the future.*2069

*Let us go into some problems.*2075

*First example, if we want to visualize the distribution of uploaded photos should we use dot plots or histograms?*2077

*Let us think about uploaded photos, is that like months where there is sort of this set finite number?*2085

*Or is it more like friends? the variable friends where there is like a ton of potential values?*2094

*Uploaded photos I’m pretty sure that people have up to like thousands of uploaded photos sometimes.*2102

*I'm thinking that it looks more like the distribution of friends than it looks like months.*2108

*Uploaded photos because there are so many values we would probably want to use grouped histograms as well.*2118

*We probably do not want to look at every single value.*2129

*How many people have one photo?*2132

*How many people have two photos?*2133

*How many people have three photos? All the way up to like thousands.*2135

*Instead we would probably want to look at them in a grouped way.*2137

*How many people have between the 0 and 500 photos?*2141

*How many people have between 500 and 100,000 photos?*2145

*And why? mostly because there are going to be a lot of potential values.*2150

*Values is what we always plot on our X axis and whenever you could sort of imagine these values*2166

*being like cut up into like thousands of pieces, you probably want to use grouped histograms.*2175

*Example number 2, consider this dot plot with the age of pennies in a sample collected by a statistics class.*2182

*What are the cases and the variables that you see here?*2189

*It is really asking you what does each little dots in my dot plot represent?*2193

*Well I know that each dot probably represents a penny but not just a penny, it has to be some sort of number about the penny.*2200

*I can see it actually the case is the penny and the variable that it has is the age, probably in years.*2211

*Because that was written on the penny it says like this penny was made in 2010.*2229

*What is the shape of this distribution?*2238

*This looks to me if I just draw a little outline here, it draws outline, this looks to me like a tail.*2241

*I'm guessing this is the right skewed distribution.*2254

*And why does it have this distribution?*2262

*That is going to take a little bit of thought.*2266

*It looks to me as though lots of pennies that is in circulation pretty new and then there are as many old ones.*2268

*Maybe it is because there is this wall right here.*2280

*Penny cannot be any newer than 0 years old.*2284

*You cannot quite go past that and probably a lot of pennies that are really old sort of fallout of circulation*2291

*or maybe the US Mint takes them out of circulation.*2298

*That is what I would answer.*2305

*Let us go onto example 3.*2309

*Considering this histogram of mammals speeds is this a grouped or ungrouped frequency distribution?*2310

*Well to me it looks like there are bins here, this is a probably a bin that goes from 0 to 10 and this is between 10 and 20.*2319

*This is between 20 and 30.*2331

*In here there might be animals that go are able to run at 23 mph or 28 mph.*2334

*I would say that this a grouped frequency distribution.*2343

*This is a good question, if we used relative frequency will this change the shape of our distribution?*2349

*Well let us reason about that a little bit.*2356

*These peaks right here, these animals are running at speeds of between 30 to 50 mph and that seems to be the mode.*2360

*The most frequent type of mammal and that is probably not going to change if you take 6 and divided it by however many animals are here.*2371

*This should still be the peak and this should still be the peak.*2384

*This should still be one of the lower values.*2388

*This should still be one of the lower values.*2391

*I’m going to say that this would not change.*2394

*No it would not change the shape of our distribution.*2397

*I have made the relative frequency distribution down here and you could see*2401

*that even when we put it in percentages that the shape of it looks largely the same.*2411

* That is one handy thing to find out that, that when you use relative frequency the distribution does not change.*2422

*We are going to be using that in the future.*2428

*Last example, in this histogram of life expectancy which do you think is bigger?*2431

*The mean or remember it is like the balancing point of this distribution or the mode the most frequent value, explain.*2437

*In this histogram of life expectancy the mode is probably the easiest thing to figure out at first.*2447

*We could see right here the biggest peak is under at around 70 in life expectancy.*2454

*Each of these little bins look like they are 4 years.*2463

*This is probably between 68 and 72 years.*2469

*That is the mode but where do you think the mean might be?*2477

*We have to imagine taking this whole thing, cutting it out with cardboard and trying to balance it on your finger.*2483

*I think that we probably have to balance it somewhere here but not too far down, not quite in the middle but somewhere right here.*2490

*That is what I’m going to guess and that might be the mean.*2503

*This is the mode.*2509

*Because if I put my balance right here, I think it probably tip on this side.*2512

*I probably shifted over a little bit and this looks like my mode is my bigger value than my mean.*2522

*Explain.*2535

*I think I have already explained it right?*2537

*My mode is right here but my mean is a little bit over here because*2542

*I think that if I balanced it right underneath the mode, it would tip on that side.*2543

*There would be too many people here on this side.*2551

*I’m going to move over my mean and because of that I can clearly see that my mode is bigger.*2554

*There you go.*2560

*Thanks for using www.educator.com.*2561

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Post by Roland Amofa on June 25, 2016

Can we have the lecture slides in a pdf format?

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Post by Ray Gaytan on October 30, 2015

Thank you, very much! Very helpful

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Post by steven bain on December 5, 2013

The exercise files seem to wrong or missing altogether.

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Post by Kathleen Donovan on April 11, 2010

Professor Yates, you're great! I like all your videos on Statistics and they are extremely helpful! I would definitely recommend them. Previously I used Youtube videos but these are definitely worth paying for --though I'm all for free education:)

Kath