Calculate average of more stages

Example:


One population has X amount of blond people, X amount light brown people, X amount of dark brown and X amount of black haired people. How to calculate the average "lighthair-ness" of that population?


The formula must take all numbers into account and number of blonds must elevate the average more than number of light browns. Likewise the number for black hair must lower the average more than number of dark browns.

One could simply take the ratio of blond vs black, but that does not tell you anything about the ratio of light brown vs dark brown. I was thinking of taking the ratio of both the extreme stages and the middle stages and then and joining it with the ratio of the middle stages by giving the extreme stages twice more importance, but it doesn't seem to work. Also what about if you have more stages or an uneven number of them?

I'm sure there is a formula.


Thanks in advance

David788 said:

Example:


One population has X amount of blond people, X amount light brown people, X amount of dark brown and X amount of black haired people. How to calculate the average "lighthair-ness" of that population?


The formula must take all numbers into account and number of blonds must elevate the average more than number of light browns. Likewise the number for black hair must lower the average more than number of dark browns.

One could simply take the ratio of blond vs black, but that does not tell you anything about the ratio of light brown vs dark brown. I was thinking of taking the ratio of both the extreme stages and the middle stages and then and joining it with the ratio of the middle stages by giving the extreme stages twice more importance, but it doesn't seem to work. Also what about if you have more stages or an uneven number of them?

I'm sure there is a formula.


Thanks in advance

Click to expand...

You know how to use your text-book or Google - find it!!

David788 said:

One population has X amount of blond people, X amount light brown (-haired) people, X amount of dark brown (-haired), and X amount of black-haired people. How to calculate the average "lighthair-ness" of that population?

Click to expand...

I will guess that, by "the average 'lighthair-ness' of that population", the book means "the probability that a given person has light hair. Since the four groups are of the same size ("X amount") and since there are four groups, when wouldn't the probability be 25%?

David788 said:

The formula must take all numbers into account and number of blonds must elevate the average more than number of light browns. Likewise the number for black hair must lower the average more than number of dark browns.

Click to expand...

Could you give us a hint what your book means by this? I mean, the number for each group is what it is. How could any valid probability formula for one of the groups change the (fixed) numbers for the other groups? :shock:

stapel said:

I will guess that, by "the average 'lighthair-ness' of that population", the book means "the probability that a given person has light hair. Since the four groups are of the same size ("X amount") and since there are four groups, when wouldn't the probability be 25%?


Could you give us a hint what your book means by this? I mean, the number for each group is what it is. How could any valid probability formula for one of the groups change the (fixed) numbers for the other groups? :shock:

Click to expand...

No you misunderstood. Imagine if you have say 7 different populations all with different percentages of those four hair color stages. How do you rate them in order from the lightest haired one to the darkest and assign a number?

The formula would be designed so that:
% of Black hair in the population would lower the final number of the formula result the most, dark brown lower it slightly less. Likewise light brown would raise it less than blond.

For example if one population has

20% blond hair
30% light brown
40% dark brown
10% black

ratio of blond vs back (extremes) is 2:1 or 2
ratio of light vs dark is 1:1 or 1

but population 2 has

10% blond
50% lightbrown
20% dark brown
20% black

ratio of blond vs black (extremes) is 1:2 or 0.5
ratio of light vs dark is 60 : 40 or 1.5

If you go by light vs dark the second population is lighter haired, but by extremes the fist population is lighter and since extremes matter more the fist would win. In this case it is quite simple, and you don't need a formula. But in real life you can have more stages than four and an uneven number of them complicating the issue. In the formula the ratio of extremes would matter most, than the ratio of first in-between stages than the (possible) more stages of further in between etc.

I hope now you understand.