Math Is Fun Forum

tina123

Member

Registered: 2012-04-29

Posts: 83

meaning of mean, mean as cluster, mean as centriod

What does mean by mean?
What is the actual meaning of mean?
Let say you have 10 points like this

9, 5 , 8,10,8,7,11,8,4,6,9,11,4

Where would be the mean?

another example

9, 5 , 8,10,8,7,11,8,4,178,9,11,20

Kindly, tell where would be the mean?

Can we say that mean value represents the all number of values?
or we will say that mean is the average of the nearest number?

like in this example
9, 5 , 8,10,8,7,11,8,4,6,9,11,4
mean would near to these values
like in this example,.
9, 5 , 8,10,8,7,11,8,4,178,9,11,20
mean would be near the values but would not go to the so different values with others . like 20 and 178..i meant outlair.

Can we say that mean represent the cluster?

Can we say that mean represent the cluster?

Mean is also called centro-id of points. Right ,

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: meaning of mean, mean as cluster, mean as centriod

Hi tina123;

The mean of the first one is 100 / 13.

The second group of data has a mean of 288 / 13.

The mean is just the average of all the numbers.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: meaning of mean, mean as cluster, mean as centriod

hi tina123

The diagram below shows one way to think about the mean.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: meaning of mean, mean as cluster, mean as centriod

and this diagram shows a centroid G

There is a weightless beam pivoted at one end, A.

There are three weights on the beam;  4 Kg at a distance 2 units from A, 3 Kg at a distance 4 units from A, and 3 Kg at a distance 6 units from A.

The total weight is 10 Kg.

The centroid is the point on the beam at which 10 Kg would give the same turning moment.

(note: turning moment is weight x distance )

moments about A:  4 x 2 + 3 x 4 + 3 x 6 = 8 + 12 + 18 = 38.

OR : total x AG => AG = 38/10 = 3.8

Bob

ps.  Don't know what to do for 'cluster'. 

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob