We will now begin our journey

into the world of statistics, which is really a way

to understand or get our head around data. So statistics is all about data. And as we begin our journey

into the world of statistics, we will be doing

a lot of what we can call descriptive statistics. So if we have a bunch

of data, and if we want to tell something

about all of that data without giving them

all of the data, can we somehow describe it

with a smaller set of numbers? So that’s what we’re

going to focus on. And then once we

build our toolkit on the descriptive

statistics, then we can start to make

inferences about that data, start to make conclusions,

start to make judgments. And we’ll start to do a lot

of inferential statistics, make inferences. So with that out of

the way, let’s think about how we can describe data. So let’s say we have

a set of numbers. We can consider this to be data. Maybe we’re measuring

the heights of our plants in our garden. And let’s say we

have six plants. And the heights are 4 inches,

3 inches, 1 inch, 6 inches, and another one’s 1 inch,

and another one is 7 inches. And let’s say someone just

said– in another room, not looking at your

plants, just said, well, you know, how

tall are your plants? And they only want

to hear one number. They want to somehow

have one number that represents all of these

different heights of plants. How would you do that? Well, you’d say, well,

how can I find something that– maybe I want

a typical number. Maybe I want some number that

somehow represents the middle. Maybe I want the

most frequent number. Maybe I want the number

that somehow represents the center of all

of these numbers. And if you said any

of those things, you would actually have

done the same things that the people who first came

up with descriptive statistics said. They said, well,

how can we do it? And we’ll start by thinking

of the idea of average. And in every day

terminology, average has a very particular

meaning, as we’ll see. When many people

talk about average, they’re talking

about the arithmetic mean, which we’ll see shortly. But in statistics, average

means something more general. It really means

give me a typical, or give me a middle number,

or– and these are or’s. And really it’s

an attempt to find a measure of central tendency. So once again, you have

a bunch of numbers. You’re somehow trying

to represent these with one number we’ll call

the average, that’s somehow typical, or middle,

or the center somehow of these numbers. And as we’ll see, there’s

many types of averages. The first is the one that you’re

probably most familiar with. It’s the one– and

people talk about hey, the average on this exam

or the average height. And that’s the arithmetic mean. Just let me write it in. I’ll write in yellow,

arithmetic mean. When arithmetic is a noun,

we call it arithmetic. When it’s an adjective like

this, we call it arithmetic, arithmetic mean. And this is really just the

sum of all the numbers divided by– this is a human-constructed

definition that we’ve found useful– the sum of

all these numbers divided by the number of

numbers we have. So given that, what

is the arithmetic mean of this data set? Well, let’s just compute it. It’s going to be 4 plus

3 plus 1 plus 6 plus 1 plus 7 over the number

of data points we have. So we have six data points. So we’re going to divide by 6. And we get 4 plus 3 is 7,

plus 1 is 8, plus 6 is 14, plus 1 is 15, plus 7. 15 plus 7 is 22. Let me do that one more time. You have 7, 8, 14, 15,

22, all of that over 6. And we could write

this as a mixed number. 6 goes into 22 three times

with a remainder of 4. So it’s 3 and 4/6, which is

the same thing as 3 and 2/3. We could write this as a

decimal with 3.6 repeating. So this is also 3.6 repeating. We could write it any

one of those ways. But this is kind of a

representative number. This is trying to get

at a central tendency. Once again, these are

human-constructed. No one ever– it’s

not like someone just found some religious

document that said, this is the way that

the arithmetic mean must be defined. It’s not as pure

of a computation as, say, finding the

circumference of the circle, which there really is–

that was kind of– we studied the universe. And that just fell out of

our study of the universe. It’s a human-constructed

definition that we found useful. Now there are other ways

to measure the average or find a typical

or middle value. The other very typical

way is the median. And I will write median. I’m running out of colors. I will write median in pink. So there is the median. And the median is literally

looking for the middle number. So if you were to order

all the numbers in your set and find the middle one,

then that is your median. So given that, what’s the

median of this set of numbers going to be? Let’s try to figure it out. Let’s try to order it. So we have 1. Then we have another 1. Then we have a 3. Then we have a 4, a 6, and a 7. So all I did is

I reordered this. And so what’s the middle number? Well, you look here. Since we have an even number of

numbers, we have six numbers, there’s not one middle number. You actually have two

middle numbers here. You have two middle

numbers right over here. You have the 3 and the 4. And in this case, when you

have two middle numbers, you actually go halfway

between these two numbers. You’re essentially taking the

arithmetic mean of these two numbers to find the median. So the median is going

to be halfway in-between 3 and 4, which is

going to be 3.5. So the median in

this case is 3.5. So if you have an even

number of numbers, the median or the middle two, the–

essentially the arithmetic mean of the middle two, or

halfway between the middle two. If you have an odd

number of numbers, it’s a little bit

easier to compute. And just so that

we see that, let me give you another data set. Let’s say our data

set– and I’ll order it for us–

let’s say our data set was 0, 7, 50, I don’t know,

10,000, and 1 million. Let’s say that is our data set. Kind of a crazy data set. But in this situation,

what is our median? Well, here we have five numbers. We have an odd

number of numbers. So it’s easier to

pick out a middle. The middle is the number that is

greater than two of the numbers and is less than

two of the numbers. It’s exactly in the middle. So in this case,

our median is 50. Now, the third measure

of central tendency, and this is the

one that’s probably used least often in

life, is the mode. And people often

forget about it. It sounds like

something very complex. But what we’ll see

is it’s actually a very straightforward idea. And in some ways, it

is the most basic idea. So the mode is actually the most

common number in a data set, if there is a most

common number. If all of the numbers

are represented equally, if there’s no one single

most common number, then you have no mode. But given that

definition of the mode, what is the single most common

number in our original data set, in this data

set right over here? Well, we only have one 4. We only have one 3. But we have two 1’s. We have one 6 and one 7. So the number that shows up

the most number of times here is our 1. So the mode, the most typical

number, the most common number here is a 1. So, you see, these

are all different ways of trying to get at a typical,

or middle, or central tendency. But they do it in very,

very different ways. And as we study more

and more statistics, we’ll see that they’re

good for different things. This is used very frequently. The median is really good if you

have some kind of crazy number out here that could

have otherwise skewed the arithmetic mean. The mode could also be useful

in situations like that, especially if you do

have one number that’s showing up a lot

more frequently. Anyway, I’ll leave you there. And we’ll– the next few videos,

we will explore statistics even deeper.

Lol funny statistics seem to be used for lots of evil ways haha :I

Thanks you bro!! Its so easy and i actuallt needed thid for my test thanks

Could you tell me , how to make these videos, As i have to make some , for some subject, but in the same format , Black background, with coloured pens, and audio, please if any body can help

Thank you! I took statistics many moons ago and needed a refresher. This is wonderful! Life does not have to be complex but so many 'intelligent' folks believe differently!

Cool! But needs to be energetic while speaking

thnx know it but need to study

Taking this next Spring, need a year to prepare. Thank you.

Nice refresher, awesome video!!!!!

lul

That was a good video

Is Rotogenflux Methods effective to your IQ score increased over 15 points? We have learn numerous good things about Rotogenflux Methods (just google search it).

RIP

my kids will love this

They are kid kid hate learning

thanks a lot

i wish i started watching the vids of khan academy years ago.

You are wonderful. Worthy

it will be very useful for Sri Chaitanyas

Or if you want to sound really fancy and posh you can say "arithmetic" in the way it sounds when it's an adjective, but when referring to it as a noun. Like "We shall study… arithmehtic!" Super posh.

6th grade? I need help with college-level statistics :/

This is so good

Thank you so much for these videos! I went from a D math student to a B math student!!!

What is the Arithmetic Mean? More like the arithmetic MEME.

you're better than my teacher 😂😂

6th year?? lmao im just learning this and im in my 9th year 😂😂

This isnt the stats I was looking for haha, I needed stats for 12th grade.

i need help with statistic… I am having major problems…HELP…Somebody anybody….please..

HELP MEEEEEE my mom is making me do khan academy and i hate this subject UGHHHHHHHHH

its kind of a shame that this Statistics class was supposed to be for 6th graders and yet we are studying this for third year engineering class……..

lol statistics

Im in +1 😂

can u reply to me

wow so good i like your teaching

I took statistics in university wish me good luck

Which 6th grader learns this stuff?

thanks for the video it helps a lot.

It’s all wrong I’m in high school and I can tell

Jeez my batch skipped grade 6 because of the k to 12 program and now, our teachers just introduced us to statistics in grade 11 0____0

0 7 50 10 000 1 000 000

~~median~~50. You should've chosen 10 0006th grade? I wish I'd done this in 6th grade…

If you think this is more helpful then school leave a like to HIM not me HIM

4:46 oh the meme mah bois

Good vid good vid

7:55–8:53 is he high his mouse keeps twitching ; 0

Thnx dear for this base method

your the best person who explain all different areas of mathematics instead of wishing my father could be alive… I wish I could meet u….that's my wish..thank you very much u have helped me alot in this subject and I hope that what u have teached others have or will learned thanks again

Iam very happy I am understanding your speech sir thank u so much

What if the set of numbers were in decimal form?

Please reply. I need help.

I like Sal so much, thanks for all your help Khan academy

I have a my stats exam tomorrow

Ohh that's nice one that I have ever watched in my carrier

which is better

Hindi chuya

I had a look a ALOT of differesnt videos and websites and more. And you "Khan Academy" are the only one that I really understand. THANKS

what if a data set has more than one mode, or none? can there be multiple numbers or an empty set?

Your better than my teacher!!!!!!!😀

Lol I am a tenth grader and this was very helpful thanks!!

im a 9th grade IGCSE preparation student and 6th graders took what i am taking… in the syllubus of IGCSE

I am not grting the consept how much i watch

Yeahh. I also don't agree with that 6th grade .. i'm in 2nd year now i have to deal with this statistics in sociology subject .. i rally don 't get it..🤔

I wrote some JavaScript functions to get mean, median and mode. I am sure they are far from perfect, but it was lots of fun to write them! : D

const meanCalculator = (numberSet) =>

numberSet.reduce((total, current) => {

return total + current;

}, 0) / numberSet.length;

const medianCalculator = (numberSet) => {

numberSet.sort((a, b) => a – b);

if (numberSet.length % 2 !== 0)

return numberSet[Math.floor(numberSet.length / 2)];

return meanCalculator([numberSet[numberSet.length / 2 – 1], numberSet[numberSet.length / 2]]);

}

const modeCalculator = (numberSet) =>

numberSet.filter(e =>

numberSet.indexOf(e) !== numberSet.lastIndexOf(e)

);

helped a lot but what if there's 2 modes

i hate math

not good

1:13

eggplant emojiwhat software does this blackboard thing? Very nice !!!

You have a great voice !

Is the average 4??

Were you the lead singer of Crash Test Dummies?

you saved my life thanks

What is the mean if we have data like this " 1 1 1 3 4 4 4 6 8"

Hello need help pls i need 10 question and answer about statistic in grade 10 lesson

Thank you sir ….for uploading this video 😎😎😎😎

I was assigned this for my 6th grade academic pentathlon and this is very useful!

6th grade? I'm a Jr in Highschool… RIP

this is the fifth time im learning this…halp

better than schools and i am in prep 3 and learning from you better than the school

I learnt this in class 6 but now in class 9 also they are teaching the same thing

This has to be the most boring subject in Maths. Awful.

I'm in my 3rd year of university and this is my first time ever studying statistics…

Supereb video

this is very helpful, but still im on seventh grade statistics

Hello thumbs up

best i bro

I'm a grade 5 student and this is our lesson (ITS SOO HARD)

2019 Anyone???

Hi,

I am trying to build my own youtube channel with my video tutorials, in a different subject than the one you present here.

Could you share with me any suggestions on the hardware & software setup you use to record these videos?

Do you use an E-drawing tablet plugged into your PC?

Do you use an independent mic (eg an USB one)?

Do you then record the whole screen session from your PC, or do you have a specific software that lets you record only the vide itself from the E-drawer?

I like the colour effects you use; could you share the model of the E-drawer tablet you use?

Thanks!

Vitus

I studying this in seventh grade😂😂😂

I know I'm late.

Let's all let it out together now.

1

2

3

Oooooh….That's how it works..

how intresting mate (in a sarcastic voice )

I want the +A,and l thinking that I am in the right direction 😌💕

I am a junior in college, I think you will be saving my grade. Thank you!

Thank you I appreciate this because I need to know stats to get my degree in TV Productions 🙂

Bless you Khan Academy

Can i do o level statatics course

What if two numbers appear twice and are tied for most number of appearances in a set of data? Do both become the mode? pls reply

got A+

Dude! I'm in my first year of college (after being out of school for 20 years) and why can't you be my instructor?!? Seriously! I now understand "6th grade" statistics! lol. Thank you so much KHAN ACADEMY!!

Thank You BTW I need this for my quiz bee tommorow thanks a lot!

I LIKE THIS WOOOO

Awsm teaching

Thank you for making free videos