Math: Define average for me

[IHateMyJob2004]

Someone just broke my brain. How do you define average? I will update this thread later with what I was told. I want everyone elses unbiased opinion on this.

Calculate the average of:
1,2,3,12,12

UPDATED :
The other party said that average meant mean, median or mode. That those 3 things are all defintions of average.

 

[Uhtrinity]

sum of the numbers divided by the # of numbers

 

[IHateMyJob2004]

sum of the numbers divided by the # of numbers

OK, that is one answer. A co-worker says there are two other formulas.

 

[mvbighead]

6, what do I win?

 

[IronWing]

Average usually is used to indicate the univariant mean. Given a series of n values of x, the mean is the sum of the values of x divided by n.

mean = SUM(x)/n

 

[RPD]

^ beat me to it. Median and average/mean aren't the same thing.

 

[IronWing]

OK, that is one answer. A co-worker says there are two other formulas.

Need more info on the context.

 

[Gibson486]

sum divided number of quantities...

 

[mvbighead]

OK, that is one answer. A co-worker says there are two other formulas.

Co-worker is either an idiot, or a mathematician.

The average is always the sum of numbers divided by the count of the numbers. I can assure that the excel function does not have more than one way to calculate the sum.

What are the answers provided by the co-worker?

 

[FirNaTine]

sum of the numbers divided by the # of numbers

That would be the mean.

Also median would be 3 (half above and half below). Used to minimize effects of outliers on the mean.

12 would be the mode. The value that occurs most frequently.

 

[Gibson486]

in before this turns into a geek thread....

 

[IHateMyJob2004]

^ beat me to it. Mean and average aren't the same thing.

This is what my coworker was saying. But I don't knwow what you are referring to with '^'. What else can average actually mean (no pun)?

 

[IHateMyJob2004]

Need more info on the context.

No, there really is not other context.

 

[Atomic Playboy]

The mean, median and mode are all technically averages; when the word average is used on it's own, it is most often used to signify the mean average. If someone asked me to find the average of a set of numbers, I would assume they meant the mean.

 

[crownjules]

What are the answers provided by the co-worker?

Must be median and mode. Can't think of any other averages for a sequence. Though I'm no mathematician.

 

[CPA]

right, coworker is probably saying mean, mode and median are all averages.

 

[IHateMyJob2004]

That would be the mean.

Also median would be 3 (half above and half below). Used to minimize effects of outliers on the mean.

12 would be the mode. The value that occurs most frequently.

THIS IS IT! But I have never referred to someone saying that mode and median as being the definitions of average.

 

[vi edit]

So does the calculator take off from the treadmill or not?

 

[Gibson486]

one is the center, the other is a statiscal norm.

 

[mvbighead]

Actually, just wiki'd and must say I am shocked:

http://en.wikipedia.org/wiki/Mean#Arithmetic_mean_.28AM.29

There are each of arithmetic, geometric, and harmonic means. Given a sample set of values, each calculates a different mean. I am not a mathematician, so the shit is greek to me.

EDIT: Each does use the word average in their definition... hmmm.

 

[Gibson486]

So does the calculator take off from the treadmill or not?

it really depends if the calculator has enough functions to support the treadmill....

 

[crownjules]

I peaked at wiki. The only other thing is that he's breaking down the different types of mean (average) - arithmetic (your usual average), geometric, and harmonic. But that's really splitting hairs.

e;fb

 

[IHateMyJob2004]

Actually, just wiki'd and must say I am shocked:

http://en.wikipedia.org/wiki/Mean#Arithmetic_mean_.28AM.29

There are each of arithmetic, geometric, and harmonic means. Given a sample set of values, each calculates a different mean. I am not a mathematician, so the shit is greek to me.

EDIT: Each does use the word average in their definition... hmmm.

Yes, I found that also. My co-worker was referring to mean, median and mode though. All defintions of average.

 

[IHateMyJob2004]

I peaked at wiki. The only other thing is that he's breaking down the different types of mean (average) - arithmetic (your usual average), geometric, and harmonic. But that's really splitting hairs.

e;fb

Nope, not the hairs he was splitting.

I did more looking up of things. There is something called central tendancy. That is mean, median and mode.

But even wikipeida presents it as kind of a grey area.

http://en.wikipedia.org/wiki/Average

But hte word average does not appear once on this page:
http://en.wikipedia.org/wiki/Median

 

[RPD]

This is what my coworker was saying. But I don't knwow what you are referring to with '^'. What else can average actually mean (no pun)?

The ^ is a visual way of referencing the post above the current one.