- 00:02
Hello.Welcome to this section of the Statistics Tutor.Here, we're going to continue talking about frequencydistributions, just giving you a little more practice,introducing a couple of additional concepts.None of them are hard, but I wantedto break it up from the last sectionand let you digest the basic concept.Here, we're going to get into justa couple of additional things.So, we've talked about the frequency,

- 00:24
we've talked about the classes, we'vetalked about writing down the class widths,and things like that.Now, I need to talk about somethingthat sounds complicated, but it's not complicated.It's called a relative frequency.

- 00:44
What it is is the percentage of the data setthat falls in a class.

- 01:06
So, it's the relative frequency.So, notice that there's a percentage involved.Basically, what relative frequency does is,it's another way of representing your frequency distributionin terms of some percentages, which can reallyhelp visualize very easily what's going on with the data.Because, don't forget, the main reasonwe use frequency distributions is

- 01:27
to take a large amount of data and make it easily digestible.So, if I had to write this down, the relative frequency-- I'llsay RF, like this-- is equal to the classfrequency over the sum of the frequencies.

- 01:49
All the frequencies added together.So, I say sum-- I have this big symbol here,you'll see what that means in a second-- of the frequenciesin all of the classes.This symbol right here just meansI'm adding up all the frequencies in my table.The symbol here, the sigma here, youneed to get used to seeing that.When you see it, it just means you add lots of things

- 02:10
together.Now, also remember, just to point something out to you,earlier we said that, when we have a frequencydistribution like that, all the frequencies are listed.Those are just the data that we've collected,we've put to different buckets.If we add up all the frequencies,that just means how many people responded.That's the sum of all of our raw data.So, when we add up the frequencies, that this is also

- 02:35
called the sample size, n.n is typically used to represent sample size.Don't worry so much why we call it n.It's just a letter.So, the relative frequency is the class frequency

- 02:56
divided by all of the frequencies in your table.Now, this looks complicated.It's very, very simple.Let's go ahead and come over hereand look at the frequency distributionof the age of people when buying first car.

- 03:22
Notice, a lot of the frequency distributionsthat I've been using are like, the ages of people.A frequency distribution can be used for anything numeric.I like to use ages a lot in these examplesbecause they're easy for you to visualize and suck itin and understand what it's talking about.So, here is our distribution.We have a class.

- 03:44
We have a frequency.And then, over here, we're going to do this part later,but we have a relative frequency.So let me put a line under there, a lineunder there, a line under there.And let's write our classes down.

- 04:05
15 to 18, 19 to 22.23 to 26.27 to 30.31 to 34.So, that's just the buckets that we've chosen there.Now, what is our data?We've taken the survey, we've figured out what we have,

- 04:26
and we're going to put everythinginto different buckets.So, we have 2 people that bought their first car in that agerange.We have 7 people that bought their first car in that range.4 people bought their first car here.Turns out, lots of people in our particular surveybought their first car in the range of 27 to 30.And here, we have fewer people here.

- 04:46
So, it looks like the bulk of peoplebought in their upper 20s for this particular group of peoplethat we have.What we're trying to do is find the relative frequency.So, the relative frequency is whatever the class frequency

- 05:08
is divided by the sum of the frequencies.So, if I take the sum of the frequencies,I can just add these guys up.The sum of these frequencies, if I add them all up,is going to be 15 plus 4 plus 3 plus 7 plus 2.And, when you do that, you're going to get 31.

- 05:31
So, that's the sum there.So, the relative frequency of this first classis the class frequency, 2, over 31.And, when you take 2 and you divide it by 31,you get 0.0645.But, we know that, when we're doing relative frequency,we want to express it as a percentage.

- 05:51
So, what we do is we move this decimal point two times,because it's like multiplying by 100.So, we multiply by 100.That moves it two times, so it's 6.45.So, what we're going to get up here, just to show our work,it'll be 2/31, which means it's going to be 6.45%.So, we do the division and we multiply by 100

- 06:12
to get a percentage.For this class, it's going to be 7/31.And then, whenever you do that division and multiply by 100,you're going to get 22.58%.When you do this guy, you'll have 4/31.And when you do that division, you'll get 12.90%.

- 06:37
And when you get this one, it'll be 15/31.And when you multiply by 100, you'll get 48.39%.And then, here, you have 3, so 3/31.And then, what you'll get 3 multiplied by 100, 9.68%.So, you see, all we're doing to get relative frequency-- itsounds like such a complicated concept-- all we're doing

- 06:60
is we're taking the frequencies, dividing by the sum,and then you get a number, and you multiply by 100,and we get a percentage.And so, what we're going to find is,if you add up all these percentages-- if you take 9.68plus this plus this plus this plus this-- you'll get 100%,because that's everything.That's everything in our table.It should be 100% when we add it all up.

- 07:21
Now, the reason we relative frequencyis because it's very nice.I can cover this up, and I can look at this table,and I can really get a nice idea of what's going on here.But, if I just look at the relative frequency,I can almost even figure it out faster.I can see, say, that 48% of the peopleare buying a first car in that range there.

- 07:42
12% is there.9% is there.22% is there.And it's just a very quick, easy waywithout really having to understand the underlyingdata very much.Everybody can understand a percentage.So, that's why we use that a lot of times.That's what relative frequency is.And that's why it's called relative.It's basically comparing the frequency of each class

- 08:03
to all of the frequencies, getting a relative indication,which we call a percentage.It basically tells you how important class is.You can figure it out here as well,but you can quickly look with a percentage.Even if some executive or CEO hasno idea what you're talking about,they will always understand a percentage.And that's really why we use it, to make it easier

- 08:24
to understand.So, the last thing we're going to talk about in this sectionhere is the cumulative frequency.This one is not used nearly as much as the relative frequency,but it's something you might be asked.

- 08:45
It's the sum of a frequency for a classand all previous classes.

- 09:11
So, just to make it easy for you,you know I like using ages.So, the age when getting the first job.If that's my data, then I might have a frequency distributionthat looks something like this.I might have class.I might have the frequency.

- 09:33
And I might have the cumulative.The word "cumulative" should mean "addition" to you.And that's exactly what it is.So, if I have a class 15 to 19, and then 20 to 24,

- 09:57
and 25 to 29, 30 to 34 and 35 to 39,my frequency data might look something like this-- 12, 8,15, 12, and 9.Now, the cumulative frequency-- I'll do it in green--

- 10:18
is the sum of the frequency for a classand all previous frequencies.Well, the first class is 12, so the cumulative frequencyis still going to be 12.For this class, what I do is, I take the 8and I add it to the 12.And I'm going to get a 20, because it's cumulative.Here, I'm going to take the 15 and I'mgoing to add it to everything that came before it.

- 10:38
So, I'm going to get 35.Here, I have 12.I'm going to add the 12 to everything that came before it.And I'm going to get 47.Here, I have a 9.I'm going to add it to everythingthat came before it and I'm going to get 56.So, it's literally just taking the classthat you're looking at and adding itto the previous classes to arrive

- 10:58
at the cumulative frequency.This is not used as much.It might be useful if you have a frequency distribution thathas classes, but you might be interested in lookingat even broader classes.So, for instance, right now, this guyis broken up into 15 to 19, 20 to 24, 25 to 29.

- 11:20
So, this is the right informationthat I have right here that lists everythingin those classes, but what if, for whatever reason,I'm really interested-- what is the frequency of everybodyless than 30 years old?And their age when getting a first job?What if I'm curious what amount of people in my survey

- 11:41
answered that they got their first job whenthey were less than 30?Well, I can easily do it from here.I can say, well, these guys were less than 30.These guys were less than 30.And these guys were less than 30.So, all of these guys fall into that bucketof being less than 30.Then, I can come over here and seeright away that 35 out of the whole amount of people,

- 12:05
35 out of 56, because if you look at all these numbersand add them up, you're going to get 56.If I look at this guy here, it's telling methe frequency of this and every class before it.So, I can say, well, 35 out of 56 peoplesaid that they got their first job there.If I'm looking here, from 30 to 34,it would be 47 people answered yes, they

- 12:27
got their first job when they wereat least 34 years or younger.Because it's looking at that class and every classbefore it.It's not often used, but it's used sometimeswhen you have a lot of data and youwant to represent it in terms of a frequency distributionwith classes that are nicely arranged,but you might want to look and say,well, how many people this age and everything lower than that

- 12:51
answered yes in our survey?So, you might have another column calledthe cumulative frequency.These are the kinds of things that you mightbe asked on a quiz or an exam.They're not the kind of things that, in my humble opinion,are incredibly important in statisticswhen you get into the really advanced concepts.We're covering a lot of really important materialnow because they're bedrock material,

- 13:12
and they are important, but we'regoing to get the concepts later on that are going to,in my opinion, become more important than someof these things here.So, I'm just going to give you a couple of quick examplesso you understand the concepts, understand what they're doing,so that you can do well on your homework and your exams.Following on to the next section,we're going to do a little more legwork before we startgetting into some of the graphing

- 13:34
and some of the more mathematical partof statistics.

### Video Info

**Series Name:** Mastering Statistics, Vol 1

**Episode:** 6

**Publisher:** Math Tutor DVD LLC.

**Publication Year:** 2013

**Video Type:**Tutorial

**Methods:** Frequency distribution

**Keywords:** mathematical computing; mathematics; mathematics instruction

### Segment Info

**Segment Num.:** 1

**Persons Discussed:**

**Events Discussed:**

**Keywords:**

## Abstract

Jason Gibson explains how to calculate frequency distributions. He explains how these calculations would be useful, then provides examples to increase understanding.