Please help with stats question!

The midrange is $\frac{max(x) + min(x)}2$ - does that help you? (The histogram doesn't tell you what max(x) and min(x) are; it only tells you a range in which they fall, so that's why there is a maximum possible midrange and a minimum possible.)

The biggest possible midrange is given when the max and min are as big as possible - that is, $max(x) = 4000$ and $min(x) = 1000$. Then the midrange is $\frac{4000+1000}2$.
The smallest possible midrange is when the max and min are as small as possible; we then get $\frac{3000+0}2$.

EDITED TO ADD: The maximum possible value of max(x) is 4000, because we know that no data point is greater than 4000. The minimum possible value of max(x) is 3000, because we know that there is at least one data point in the range [3000,4000].

So, how did the answers come up to 1500 and 2500?

Because that's what you get when you evaluate the two fractions…

Oh I get it now! but still kind of confused how the max value of the min came about? do you know any website or anything that can explain this? Thanks!

I don't know of any websites or anything - it's just that if you want min(x) to be as big as possible, then it has to be 1000, because you know that there *is* an x between 0 and 1000, and you know that min(x) lies in that range; the largest possible value for the minimum is therefore 1000. Can't really think of a better way to explain it this late at night…

Haha thanks for the help! I understand the 1000, but I dont understand the 3000. Do you have any tips on alevel maths revision? I have 5 next month, and its driving me crazy!

The 3000 comes from "the smallest possible max(x) is 3000", since the histogram could perfectly well have been produced from {… 2999, 3000, 3000, 3000, (lots of 3000 to make up the right probability density)}. But the smallest possible max(x) isn't 2999, because there's no way that data ending {… 2999} could give that histogram, because we know there are things in the "3000 to 4000" bin.
I don't really have any tips apart from doing loads and loads of practice papers! Make sure your teacher looks over a few of your papers too, to check that your exam technique/way of writing up answers is fine.

Thanks for your help! I'm guessing you're currently doing a maths degree?

Haha which alevels did you do? and Where are you studying now? I have c2,s1,s2,d1,c3 - I'm gonna die! I do english as well, so not a great combination!

Physics, maths/fmaths, Latin, chemistry, computing, and Cambridge My sister did English, the workload for that was huge! At least D1 should be fairly straightforward, if you've learned the techniques well… S2 was the one I found most difficult because there were so many arbitrary things to memorise - until I found out that you can hand-wave some of them (for instance, on the "conditions allowing a normal approximation to the binomial distribution", you can just say "for n sufficiently large and for p sufficiently close to 1/2" rather than "for n>50".) What plans do you have for afterwards? Maths+English isn't particularly standard, as far as I know, so no clues there…

Oh wow that is great haha! How you finding first year? and yeah s2/c3 is most difficult for me right now because they are a2 modules, yeah d1 is really easy! but then again its easy to make a mistake aswell! Well, I do economics, maths, further maths and english literature so I want to do economics and management hopefully! I took both further maths and english because the oxford admissions officer said that you need to demonstrate both your maths skills and essay writing skills. Now, I regret taking english; I wish I did physics instead of picking an alevel just because its good for the course requirement! Ah well, nothing I can do now I guess!

First year's hard work, and it should be harder but I keep procrastinating :P It's always useful to be able to demonstrate essay skills - English is really good for that, and I imagine it would be handy in E&M. Good luck with the A-levels - I assume you're trying for Oxford then? I'm afraid I don't know much about either Oxford or economics (other than in the broad hand-waving sense), so I can't give any advice for them In C3, at least, there's only about thirty questions in total, and they just repeat them year on year with different numbers in, so loads of practice is the key.

Haha procrastination is my biggest crime Yeah I guess, but its also hard revising for something you are not passionate about! And thank you so much, Good luck with your first year! I just want to be at university, everyone says uni life beats school life by far! And well i hope so, obviously depends on my AS grades first! And thank you for the maths advice

Uni life does beat school life, I think good luck on the exams!