How do you determine the "average" of a certain value?

Question

I have checked out the Wikipedia article, but it's too complicated for me.

Also, this definition:

constituting the result obtained by adding together several quantities and then dividing this total by the number of quantities.

does not make clear sense either. First off, constituting means composed of, adding several quantities, and then dividing them also is nonsense.

If I add 60 to 0, I have 60. If I divide 60 by itself I am left with 1. However, dividing anything by itself results in 1, unless you divide by zero.

So please tell me how I get the "average" of something by "adding something", and then "dividing something" by "its quantities"?

That makes no logical sense to me.

Answer 1

To take the average of $60$ and $0$, you add the quantities $(60 + 0) = 60$, and divide by $2$: $\dfrac {60 + 0}2 = 30$, since you are averaging two quantities: $60$ and $0$.

Indeed, given three quantities, $a, b, c$, we add them, and divide by $3$.

Average: $$\dfrac{a + b+ c}{3}$$

If we have $n$ quantities, we take their sum, and divide the sum by $n$:

$$\dfrac{x_1 + x_2 + \cdots + x_n}{n}$$ to find their average.

Answer 2

The average of 4, 5 and 8 is $$\frac {4+5+8}{3} = \frac {17}{3} = 5 \frac {2}{3}.$$

Answer 3

Well basically, if you have (let's say) 3 values $x_1, x_2$ and $x_3$ the average would be $(x_1+x_2+x_3)/3$. If you have $n$ quantities $x_1,...., x_n$ the average would be $(x_1+....+x_n)/n$. Is it understandable?

Answer 4

The idea is that you are adding the quantities themselves and dividing by the number of quantities.

In your example: You add the two quantities $60 + 0 = 60$. Then divide by the number of quantites, which is $2$, to get $$ \frac{60 + 0}{2} = 30 $$

Answer 5

The wikipedia article says you add the quantities, then divide by the number of quantities, by which they mean how many different quantities you have, not their total.

If you have 30 houses, the total value of which is \$200,000, then the average value of each house is \$6666.67.

In this case, your quantities are values of houses, measured in dollars. The total sum of these quantities is \$200,000. You have 30 different houses, each of which has some value associated with it. So the number of quantities you have is 30. Therefore,

$$ \frac{\$200,000}{30 \textrm{houses}} = \$6666.67 \textrm{ per house}. $$

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You don't take the average of a value, you take the average of a set of values. There are many ways to do this, and it all depends on what you want to do.

Most people think of the average as throwing a bunch of objects in a black box, and then assuming they're all more or less the same, they want to estimate the value of a single object. For example, if you have four pumpkins of different weights on your porch, you might want to estimate the weight of a single pumpkin, assuming they're all the same. Why you'd want to do this, who knows?

There are other ways and interpretations of the average, and they're useful (or not useful) for different reasons.