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this video was specifically requested

from a commentator of another video of

mine

the person wanted more examples of

population means and so that's exactly

what i'm going to do i'm going to just

simply go over

what a parameter is in regards to the

population mean and then go through

those examples

so we have the formula at the top it's

the summation of x

i over n equals mu

which is a parameter now a parameter

is something that is true it's not an

approximation it's not something you're

guessing at

this is what it is and that's what makes

it different from a sample mean

you're not trying to approximate this

parameter

you just have it the first example is

what is the population mean

size of the seven families in your

neighborhood so you live in a

neighborhood

say you have seven families what is the

average size of those families

it's going to be a population mean

because you just have seven families in

your neighborhood you don't have

eight nine ten or eleven you don't have

three

you just have seven families so you're

getting the totality of

everything and it's gonna be crunched

into this one parameter

not a statistic and so the family sizes

in your neighborhood

are 7 1 3 2

4 3 and 4. and so how would you go about

calculating that using the formula

this is what it looks like so you have

the mu

for the parameter the summation of x i

over capital n

you have the numbers all added up here

and then you divide by the number of

families you have which is 7.

you add it up you get 24 divided by 7

you get

3.43 as the average family size in your

neighborhood

this is a real parameter that you can

have this isn't using

thousands of bits of data you can do

this in your own

area where you live to find out you know

what is your population mean for family

sizes

you know maybe it's apartments maybe

it's something else but it's a realistic

question

that you may want to know for a variety

of reasons

you know there's real world application

and knowingness

the next is what is the population mean

weight in kilograms of the 2239 people

in the city

so it's going to go over the same

process

i don't have a list of the two thousand

two hundred thirty nine people

because frankly that i would not be able

to show all those numbers without

giving you some excel sheet and the

numbers would be meaningless to you

anyway because that would just be a data

overload

so this is how it would look like in

terms of

how you're writing it just for

simplicity's sake

so you have you calculate the mu just

like before you have summation of x

i over n but you use something

to summarize the 2239 people

usually it's going to be excel usually

it's going to be something

where you can do that it's not going to

be in by hand or on paper

and then you divide by 2239 because

that's what the

population of the city is and so i've

got this

uh this total here 170 835.7

divided by 2239 divided by the

the amount of people this number is just

the summarization of the weights of

all 2239 people that's all that it is

you're just adding them all together and

then you're dividing by the amount of

people that are in the city

and it gives you 76.3 kilograms

so that's the average weight of the

people in the city

that is not a statistic it is not

something you're approximating it is

something that is true

and that is something that if you used

other statistical methods

you may use to find out say the standard

deviation

when you're dealing with parameters it's

something that is true you're not

approximating it

it's just what it is if you found this

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thank you and stay nerdy my friends