The number of ways to choose 5 cards from 10 choices = 10C5 = 252.magnus opus wrote:Five cards are to be selected at random from 10 cards numbered from 1 to 10. How many ways are possible that the average of the five numbers selected will be greater than the median?
have no clue how to solve this one under two minutes. please help.
It's clearly not a real GMAT question since there is no reasonable way to do the problem quickly. It isn't worth worrying about.magnus opus wrote:yes 111 is the correct answer, but it cannot be done in under two minutes this way.
If you find yourself tempted to use some properties of normal distributions (bell curves) on the GMAT, stop immediately and find some other approach. Normal distributions are never tested on the GMAT, and if you don't have a very solid grounding in statistics, you'll probably be misapplying what you do know. Here, for example, there's simply no reason to think the numbers are distributed along a bell curve in the first place (they are not, in fact, even 'approximately normally distributed' in the technical sense of that phrase), and I don't see how you've decided that the first case, in which the set is {1,2,3,4,5}, represents 2% of all cases - when you do that, you're simply guessing in advance that there are 50 cases, and that's exactly what we're trying to figure out.magnus opus wrote: I was thinking of of using the bell curve on such a question if the answer choices are spread out ( far apart to allow approx)
now its easy to figure out that the first case has only one possibility 12345 with mean equal to median.
so 1 case =2%, hence 14%= 7cases, 34%= 17
I suppose you could ask the reverse question: why *should* you have an equal number of each case? If I ask a simpler question:magnus opus wrote: - More important question, can you point out why we do not see an equal number of cases in all three segements namely :
mean=median; mean>median; mean<median
well the reason I applied the bell curve was that (as I already mentioned I knew the cases are 30)Ian Stewart wrote:It's clearly not a real GMAT question since there is no reasonable way to do the problem quickly. It isn't worth worrying about.magnus opus wrote:yes 111 is the correct answer, but it cannot be done in under two minutes this way.
If you find yourself tempted to use some properties of normal distributions (bell curves) on the GMAT, stop immediately and find some other approach. Normal distributions are never tested on the GMAT, and if you don't have a very solid grounding in statistics, you'll probably be misapplying what you do know. Here, for example, there's simply no reason to think the numbers are distributed along a bell curve in the first place (they are not, in fact, even 'approximately normally distributed' in the technical sense of that phrase), and I don't see how you've decided that the first case, in which the set is {1,2,3,4,5}, represents 2% of all cases - when you do that, you're simply guessing in advance that there are 50 cases, and that's exactly what we're trying to figure out.magnus opus wrote: I was thinking of of using the bell curve on such a question if the answer choices are spread out ( far apart to allow approx)
now its easy to figure out that the first case has only one possibility 12345 with mean equal to median.
so 1 case =2%, hence 14%= 7cases, 34%= 17
I suppose you could ask the reverse question: why *should* you have an equal number of each case? If I ask a simpler question:magnus opus wrote: - More important question, can you point out why we do not see an equal number of cases in all three segements namely :
mean=median; mean>median; mean<median
If you pick a random number x from the set {1,2,3,4,5,6,7}, what is the probability the number is greater than 4?
you certainly wouldn't expect it to be equally likely that x < 4, that x = 4 and that x > 4.
If you invent a set of numbers completely at random, it will be very rare that the mean and median are equal, so in the question in the original post, you'd expect the case "median = mean" to be less common that the other possibilities.
