After watching Ron's Video on CR-Numbers&Statistics-Part 1 and part2,I am bit confused about the following .
Problem 1 uses pounds per production worker
Problem 2 uses dollars per ton of coal
Problem 3 uses number of crimes per 1000 residents

My doubt:
In the Video,Ron states that
In Problem 3:"This is a per capita rate.The point of per capita rates is to get rid off the effect of poppulation size.The point of units of the form "unit1 per unit2" is generally to take out the confounding effect of unit 2."

In Problem 2:"This takes away the effect of the total volumes of mine"

But in Problem1 :"The amount of waste has gone down by 50%.This could come from
-increase in number of workers
or decrease in lbs"

WHy doesn't the effect of number of workers not taken out in Problem 1.
And why does the effect of voumes of mine or population size taken away in Problem 2 and 3 ?
In short to paraphrase : I am bit confused about when
will the denominator effect be taken away and when will the effect not be taken away.

I understand the solution stated for each of the Problem.However,when I compare the solution of these three problems ,I am still not clear on the above stated Qn.

Below is the QN stem of all 3 problems:

Problem 1:
In response to mounting pubic concern, an airplane manufacturer implemented a program with the well-publicized goal of reducing by half the total yearly amount of hazardous waste generated by its passenger-jet division. When the program began in 1994, the division's hazardous waste output was 90 pounds per production worker; last year it was 40 pounds per production worker. Clearly, therefore, charges that the manufacturer's program has not met its goal are false.


Problem 2:
Twenty years ago, Balzania put in place regulations requiring operators of surface mines to pay for the reclamation of mined-out land. Since then, reclamation technology has not improved. Yet, the average reclamation cost for a surface coal mine being reclaimed today is only four dollars per ton of coal that the mine produced, less than half what it cost to reclaim surface mines in the years immediately after the regulations took effect.

Which of the following, if true, most helps to account for the drop in reclamation costs described?

Problem 3:

The violent crime rate (number of violent crimes per 1,000 residents) in Meadowbrook is
60 percent higher now than it was four years ago. The corresponding increase for
Parkdale is only 10 percent. These figures support the conclusion that residents of
Meadowbrook are more likely to become victims of violent crime than are residents of
Parkdale.

Can someone kindly respond!

this statement means that a per-capita rate is meaningful without a corresponding figure for total population.
for instance, “3 of every 100 babies in country x died of malnutrition last year” is a meaningful statement, regardless of the population of country x -- this statement has the same import whether country x has 1 million people or 1 billion people (or whatever other population).
by contrast, the statement that “30,000 babies died of malnutrition last year in country x” is absolutely meaningless unless we know approximately how many babies were in country x.

--

the statement does not mean that you can simply ignore the underlying population size whenever you see a per-capita statistic. the population size won't be important in interpreting a single per-capita statistic, but population size can be crucially important in considering changes in per-capita statistics. if a population size can change, then such changes can definitely affect per-capita figures.

the reason that such changes are not considered in e.g. problem #3 is that the figure of 1000 residents is invariant (i.e., it can't change).

don't do this -- i.e., DO NOT post a message that says "please answer my question".
this is called "bumping" the thread; it brings the thread up to the most recent position in the folder.

the problem, of course -- besides the fact that "reminder posts" are obnoxious, rude, and unprofessional -- is that we answer the posts strictly in order from oldest to newest. therefore, if you post a message, with no content, that says "please answer this post", then you are moving the thread to the LAST place in the queue.

please be patient -- we will get to all of the threads. if you make posts like this one, you're just making yourself wait longer.

thanks.