Ryan Report -discussion of statistics.

rant_and_rave

I and a "friend" are having a discussion about some of the statistics in the Ryan Report. The Report says 170,000 children passed through industrial schools over 34 years with the average stay of each child being 7 years. It also says that the average annual number of children in the institutions was between 5000 and 6000 per year. My "friend" says the average is calculated like this 170,000/34 = 5000. I say that is only correct if each child stayed an average of 1 year in the institutions. I say that 170,000 children, each staying for an average of seven years in an industrial school gives a total of 1,190,000 person years which over the 34 year period would give an average annual industrial school population of 35,000, not 5000.

Which of us is correct?

Ostrom

rant_and_rave wrote: »

I and a "friend" are having a discussion about some of the statistics in the Ryan Report. The Report says 170,000 children passed through industrial schools over 34 years with the average stay of each child being 7 years. It also says that the average annual number of children in the institutions was between 5000 and 6000 per year. My "friend" says the average is calculated like this 170,000/34 = 5000. I say that is only correct if each child stayed an average of 1 year in the institutions. I say that 170,000 children, each staying for an average of seven years in an industrial school gives a total of 1,190,000 person years which over the 34 year period would give an average annual industrial school population of 35,000, not 5000.

Which of us is correct?

Your friend I think - you cannot multiply the average stay by the cases, as there is likely to be significant variance in the period of stay across time. Since they didnt supply the standard deviation, you have no idea of the extent to which time periods of peak occupancy, or exceptionally long or short stays affected the mean.

Same with the average occupancy per institution per year.

RoundTower

efla wrote: »

Your friend I think - you cannot multiply the average stay by the cases, as there is likely to be significant variance in the period of stay across time. Since they didnt supply the standard deviation, you have no idea of the extent to which time periods of peak occupancy, or exceptionally long or short stays affected the mean.

how would long or short stays affect the mean? Since they gave the average stay and you are looking for the average population.

For example, if my hen lays an average of four eggs a week, in any year it lays about 52 x 4 = 208 eggs. Not 52 eggs which is what one would get using your reasoning.

OP is correct, or at least closer to correct than his friend.

Ostrom

I seem to have invented and responded to my own question/interest in seeing dispersion figures, sorry. I really don't know why I wrote that...

What I meant to ask was how representative the mean is likely to be considering high variability in peak occupancy across time and institution. Are there any other stats or tables?

ray giraffe

The OP's reasoning seems precisely correct to me, variation of length of stay is irrelevant for the question.