Some reminders about checking
Whenever you have done some maths work, and especially in exams, if you have any spare time you can use it constructively to look for errors and save marks.If at all possible, try to check your result a different way from how you calculated it. Just looking at your working is not very effective, as you usually just make the same mistake.
If you have done a calculation using a calculator, try to do the same calculation in rough, using approximate numbers, to see if your calculation is close to where you expect it to be.
If your calculator shows the calculation that it has done, then double check this against the original question, especially for the brackets.
If you have just worked out the area of a complicated figure, think of a simple figure, such as a rectangle that encloses the whole shape. The area of this would be an upper bound, to see if your answer seems reasonable. Even better, you may also be able to see a rectangle which is totally within your shape. The area of that would give you a lower bound for your answer.
Algebra
If you have solved an equation then this is easy - just substitute your solution into the original equation and see if it works. If it doesn't then you have definitely slipped up and you then need to look carefully at your working to find the mistake.
If you have manipulated an algebraic expression, a very quick check is just to put a couple of simple values in, say x=0, 1, and 10, to see if the original expression and your manipulation of it, both give the same answers.
One of the most effective things you can do is just to be neat. Give yourself lots of space when you are doing some algebra, and lay out your intermediate results methodically.
Statistics
--[reporting2] Doing 'do snippet' - should be imbed--Ways of checking statistics questions
If you have time to review your work in the exam always try to check using a different approach than the one you used to do the question in the first place.
Quick reasonableness checks on the mean and standard deviation would be:
- Is the mean roughly in the middle of my data?
- Does the interval from mean-sd to mean+sd include about two thirds of my data?
Another way to check questions about mean and standard deviation is to choose a coding, one which makes the numbers as simple as possible, so that you can do most of the calculations without a calculator.
Coding works well with exam questions, where the numbers are contrived, it is less relevant in the real world where the numbers tend to be messier, but in the real world you use a computer to crunch the numbers so it doesn't matter.
Note that in the real world it is still very important to use common sense reasonableness checks if you can, like checking that the mean and standard deviation are what you would expect.
When choosing your coding look to subtract a number near the mean or mode. Choosing the mode is good because it means you will have several 0's in your coded data. Also divide by something simple (2, 10, 100) if it makes things easier, but only choose something you can do in your head.
When you have chosen your coding, write it down clearly. If you don't, you are guaranteed to make mistakes.