• ## Summary

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• 00:00

Hello.Welcome to this section of Mastering Statistics.Here, we're going to talk about some topicsthat I know all of you know at least a little bit about.But we really need to make sure and cover it because you neverknow what certain people know and what certain people don'tknow.You also want to make sure that everyonehas the same definition for some things thatseem to be common knowledge.

• 00:20

So we're going to talk about pie charts, bar charts,and something called a Pareto chartthat you might also see on your exam.So the first thing we're going to talk about is a pie chart.How many of you guys have seen, or drawn,or graphed a pie chart?Basically, a pie chart shows data-- shows raw data--

• 00:42

as fractions of a circle.That's why it's useful.So for instance, the data that we might be talking about hereis the favorite color of males.So let's say we do a survey or something-- 10,000 men.

• 01:03

We call them and say, hey what's your favorite color?Some people are going to answer blue.Some people are going to answer yellow.Some people are going to answer red.And we get all that data.And this is just a way to represent that.So what we have is we have a pie chart or a pie graph.So what we do is we draw a circlebecause pies are circles.

• 01:24

And inside of that guy, then we have certain wedges.So we have this wedge here to the center like this.This is about 10% of this pie.And I don't have enough room insideto write it so I'll write it over here.This is yellow, like this.

• 01:45

And sometimes a pie chart uses different colors.Sometimes, it's shaded.I'm not going to shade it here because I don'twant to clutter up the board.But I might have another wedge over here, which represents--if this is 10%, this is more than that-- solet's say this is 18%.And this is purple.So 18% of the people that answered our survey

• 02:09

said that their favorite color was purple.And then, we have something like this.So this guy here is 31% answered red-- something like that.And this is not to scale.You'll have to bear with me here.But let's say this is 41% of the circle.

• 02:32

And these guys answer blue.So we have some people that said blue was their favorite color.Some people that said red was their favorite color.Some people said purple.Some people said yellow was their favorite color.Notice nobody said green in our particular survey.Nobody said pink.Nobody said gray.Nobody said black.So if it's not in our pie chart, then it doesn't exist.

• 02:54

It's not an answer in our survey.So I know you guys have seen all this kind of thing before.And basically, we represent it as parts of a circle meaningthat the whole circle-- the whole pie--represent all possible answers.And we slice up that pie to represent the different slicesof the answers that we get.And notice that if we take 41% plus 31% plus 18% plus 10%,

• 03:18

we're going to get 100% because every answer in our pieshould add up to be 100%.Now, a lot of times nowadays, we use computers-- software--to make our pie charts for us.But if you had to make one of these by handto find the wedges, I think it'd be nice just to tell you really

• 03:41

quickly how to do that.So for instance, for the yellow wedge,I'm going to take a bunch of answers on the telephoneand I'm going to end up finding that 0.1of all of our answers-- 0.1 as a fraction of our answers--answered yellow.So what I do is I multiply that by 360 because thereare 360 degrees in a circle.

• 04:03

And what I'm going to get is 36 degrees.So what this means is that in orderto find out how wide this yellow wedge needs to be-- this 0.1is what I've measured in my survey--0.1 of all of my respondents.In other words, 1/10 of all of my respondents answered yellow.I take that number multiplied by 360 degrees.So then, 36 degrees must be the yellow wedge.

• 04:25

So if I put an angle measure here, that's 36 degrees.For blue, I get on the phone and figure outthat 0.41-- almost half of everybody-- answered blue.All I do is I multiply by 360.And then, what I get is 147.6 degrees.So the blue wedge here, if I get a protractor and measure it,

• 04:52

it should be 147.6 degrees.So that's how I would construct this by hand.And you basically, just keep going down the line there.So if you go purple, 0.18 of respondents,then as a fraction of everything I have-- so almost 1/5is what this looks like.You multiply by 360.

• 05:14

And then, what you get is 64.8 degrees.And then, finally, we have the red-- 0.31-- so almost 1/3of everybody that answered.I'd multiply by 360 degrees and I'd get 111.6 degrees.So what this is telling me is if I were trying to constructa pie chart or a pie graph by hand,

• 05:36

then I need to know-- as a fraction of everythingI have-- what everyone answered.I multiply by the number of degrees in a circle.And I'm going to get the number of degreesof each of these wedges.If I add up all of these degrees here-- 36plus 147.6 plus 64.8 plus 111.6--I'm going to get 360 degrees because that's how many degrees

• 06:00

are in a circle.So that is it for pie charts.We're blazing through here.We're not going to spend too much timeon this because I know that you've seen this stuff before--or most of you have.A bar graph-- I know you've seen bar graphs before.You see them on television.You see them everywhere.If I want to represent this data as a bar graph,

• 06:22

then literally, what I have to dois draw a set of axes like this.And what I'm going to have-- this will be,let's just say, 10, 20, 30, 40.So this is the percentage of people that answer.And then, what I'm going to have-- let's just changethe color.

• 06:43

Let's say I have yellow.So let's look back at our data.How many people answered yellow?It was 10%.So what I'm going to do is draw a bar right up to the 10% mark.And then, after that, I have blue.Blue was represented at 41%.That came from our data.So I'm going to go all the way up just above 40

• 07:06

because we're at 41.And there I go.My next one is red.Red looks like it was 31%.So I'm going to start here.I'm going to go up, up, up, up, up, just above 30 because I'mat 31.Draw a nice little skyscraper there.The final one is purple.

• 07:26

Purple was 18%.So I'm going to draw my little skyscraperalmost touching the 20% mark.Best I can do by eyeballing it.There's my bar graph.Notice-- a couple things I want to point outto you about bar graphs.And the reason I'm pointing these outis because we're going to end up graphing some datain a minute called a histogram.And it's going to look a little bit like a bar graph

• 07:49

but it will look different.So for a bar graph, couple of things.The bars do not touch, in general, on a bar graph.So this bar, it sits next to the blue onebut it doesn't touch it.There's a gap here.Typically, bar graphs are going to have a gap between them.The width of the bars are typically the same.I've tried to draw them as close as I can by eye to the same.

• 08:10

They should be the same width.The width of these bars don't actually mean anything.The only thing this bar is telling meis how high it is so I can compareblue, to red, to purple, to yellow.So that is what we call a bar graph.Now, I'm going to draw something you may not have heard before.It sounds hard, but it's really easy-- Pareto chart.

• 08:34

Or you might see it called Pareto graph.So all it is, is a bar graph in descending order.So really, really quickly-- here is my axis right here.

• 08:59

This is 10, 20, 30, 40-- so 10, 20, 30, 40.So if you were given a bar graph and the exam or whatever says,hey draw this as a Pareto chart, thenyou would need to know what that means.It's descending order.So the tallest one of these guys is blue.So blue would come first.And blue is up at 41.So I would go up to 41 and I would draw a bar.

• 09:23

The next tallest bar is red.So I would draw that next.It goes up to 31.So I'd go up to 31.Draw the bar graph like that.The next tallest one is purple-- whichis over here-- which is at 18.So I'd go up to 18-- about like that.

• 09:43

And then, yellow-- which if memory serves-- is 10%.So that's going to be yellow right up to about there.So basically, a Pareto chart is a bar chart.It's just that when you rearrange the bars--and in this particular case, it doesn't reallymatter so much if the bars are in this order or in this order.I mean, they convey the same information.

• 10:05

I'm just trying to pull some of these things out of your class,out of your book, that you're typicallygoing to be asked to learn so that whenever you see a Paretochart, you don't say, I see something that is complicated,because it's not complicated.So we blew through these pretty fast because theyare pretty easy concepts.I know you've seen them before.We have the pie chart.We have the bar chart.We have the Pareto chart-- which is just a bar chart.

• 10:26

And we're just trying to learn how to represent data.Typically, when a statistics class starts,you learn about collecting data; you learn definitions;you learn how to represent data; graph data-- which iskind of what we're doing now.And here, very, very soon, we're goingto start learning how to pull information outof data with calculations.So follow me on, step by step, and we'll get to those concepts

• 10:47

here very shortly.

### Video Info

Series Name: Mastering Statistics, Vol 1

Episode: 7

Publisher: Math Tutor DVD

Publication Year: 2013

Video Type:Tutorial

Methods: Pie charts, Bar charts

Keywords: mathematics

### Segment Info

Segment Num.: 1

Persons Discussed:

Events Discussed:

Keywords:

## Abstract

Jason Gibson explains how to create a variety of different charts to use in statistical analysis. He discusses the best cases for using each chart, and he completes some example charts for practice.