Terms for addable variables

Mar 2018
6
0
Europe
I wonder what parts of statistics have specific terms existing for them - I see a relevant notion which would be relevant, but not sure if there is a term for it.

If variable values can be ordered then it possesses a median.
If the values can also be added then they also possess an average.
A data set to illustrate it:
There are a bit over 7 milliard people in world.
Total wealth owned in world is 241 000 milliard US \$. It is a summable variable.

Since it is summable, it possesses average. Which comes at about 34 000 US \$ per head.

50 % of world population possesses about 1700 milliard US\$, which is about 0,7 % of the total. This the average wealth of the second half is about US\$ 500. The average wealth of the richer half is about US\$ 68 000.
The value of which 50 % people are richer and 50 % are poorer is the median.

But now to illustrate my question.
1 % of people own 46 % of all wealth - 110 000 milliard US\$. This makes about 1 500 000 US\$ per member of that 1 %.

It would be interesting to know:
1) the actual number of richest people who own, not 46 % of all wealth, but exactly 50 % of all wealth. Which is clearly a bit bigger than 1 %, but exactly what?
2) the actual value of wealth such that people richer than that possess 50 % of the wealth - obviously less than 1 500 000 US\$, but again how much?

And my question on statistics is:
are there any established terms to call the answers to 1) and 2)? How to talk of quantiles of the sum of the values, as opposed to quantiles of the number of observations?

Edit - on your board, dollar sign seems to be handled as a special sign - do not know how to actually show it.
 
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greg1313

Forum Staff
Oct 2008
8,008
1,174
London, Ontario, Canada - The Forest City
Edit - on your board, dollar sign seems to be handled as a special sign - do not know how to actually show it.
Precede '$' with '\'.
 
Jun 2019
493
261
USA
I am not familiar with any words that adequately describe those values. You would probably have to define exactly what you mean, either mathematically or in words as you have done.

Of course, you are free to come up with your own terms for them, use those terms in economic discussion/analysis, and see if they catch on or not.

(P.S., for the non-francophones, 1 milliard = 1 billion (short billion) = $10^9$.)