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Estimate the average time-length that a student is enrolled at the university (including students who graduate and those transfer or drop out)

My thought: I computed the percentage of new student, classified as either first-year or transfer, in each of year 1-5. I also computed the number of students who dropped out in each year (but I could not determine how long they stay, which is the key point). Anyway, I think we could use Little's Law ($L_i = \lambda_i W_i$), but I am stuck on getting $\lambda$ and $W$ (is $W_i$ equal to the total enrollment in year i? Similarly, is $\lambda_i$ equal to the total number of new students in year i?).

My question: I would sincerely appreciate if someone could give some thought on this problem.

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I think you are correct that this is supposed to be an exercise using and understanding Little's Law.

Average 'Enrollment', which I would view as $L$ (number in system) seems fairly stable around 17,000. So it seems realistic to assume the system is at steady state. (You can find the mean, instead of my rough guess of 17,000.)

I would view 'New Students' as providing information on $\lambda$ (rate of entry).

From $L$ and $\lambda,$ I guess you are supposed to estimate $W$ (average time in system).

If $W$ is to be average years in the system, then you have to express $\lambda$ as rate of entry per year.

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    thank you for your suggestion. Here is what I got based on it (please let me know if you think this is incorrect): we could find $L = $ total enrollment/5 $= 16800$. Now, $\lambda$ for the new students could be computed as average number of new students per year $= 4006$ Thus, $W = W_1+W_2 = 4 + \frac{16800}{4006} = 4+4.1937 = 8.1937$ ($W_1 =$ average time-length of ALL students who graduate from the university, $W_2 =$ average time-length of ALL 1st-year students and transfer students over the 5-year period). However, this calculation results in double-count between $W_1$ and $W_2$. – 2017-01-26
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    The double-count occurs for all the 1st-year student who ended up graduating. So I guess $W_2$ is defined ONLY over the transfer students, so it should be equal to $\frac{16800}{2188}$? But again, this is greater than $4$, which is intuitively wrong since a student who drop out should, on average, spend less than $4$ years in a university?? – 2017-01-26
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    I'm not sure what assumptions the author of the problem has in mind, but I think you need to focus on $λ$ as _arrival rate per year._ If many students are part-time, they will take more than 4 years to finish. – 2017-01-27
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    I thought that's what I tried to do in the solution above?? By saying $\lambda = $ arrival rate per year, did you mean I should calculate each of $\lambda_{i}$ for $i=1,2,...,5$, and from $L_i = \lambda_{i}W_i$, I could calculate $W_i$. But this $W_i$ is the average time-length of students enrolled in college in year $i$, not the entire average time-length that a student is enrolled at the university, so it's not the right way I think?? Also, could you help point out to me where my mistake was in the solution above? Your explanation on the part-time makes so much sense:) – 2017-01-27
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    I was not saying you are wrong, merely trying to eliminate distractions by focusing on the main point. (And to mention part-time students.) But, without context from the text, I'm honestly not sure _exactly_ what you are expected to do. – 2017-01-27
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    thank you for your prompt reply. The problem is stated as it is, but I have another question: regards to my W_1 above, it might be less than $4$ (some students took only $3$ years to graduate, or even $2$). So I guess because the problem said *estimate*, I would assume all students who graduate take $4$ years, which is a reasonable assumption I think. So I got $W_2$ correctly, didn't I? – 2017-01-27
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    could you please confirm if my thought above is correct? I meant, the argument I used to arrive at the answer of $8.1937$. – 2017-01-28