maximum possible ,median number
one day the Pythagoras kiosk sold 252 cans of soda to 100 customers and every customer bought at least one can of soda . what is the maximum possible median number of soda bought per customer on that day.
jag tänkte så här. 252/100=2,52 cans of soda bought per customer on that day but the right answer is 3,5 cans.
how i must think right to solve this problem
Do you know what median number is? and how you figure a medaian number out?
not really,no
Out of 100 customers. The 50th and 51st customer will be the median customers. We want to maximise their bought cans to get the maximum median. Okay so let´s say we divide the 252 cans between them. Let´s say customer 50 buys 126 cans and customer 51 buys 126 cans. BUT THAT IS NOT POSSIBLE. Because then there would be no cans for the other 98 customers and they had bought at least one each. The first 49 customers, we let buy only one can each (because we want maximum of cans left the median customers).
How many cans are left and how do we divide them between the rest of the customers to get a high median value?
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Then we have 252-49=203 cans left. So okay do we let customer 52 to 100 also buy one soda? No that is not possible because for customer 50 and 51 to be the median customers, they must have bought more(or equal) number of cans than customer 50 and 51. Hmm that is not good, because we mant the most cans for the median customers. But okay.. The very best will be if we let the customer 50 and 51 and all above them(52-100) buy the same numbers of sodas, that will also maximise the numbers of cans for customer 50 and 51. 203 cans divided for the 51 customers left(nr. 50 to 100). 203/51=3,98. Okay so we let them buy say 4 cans each. 4*51 is 204. That is one can to much. So one of them has to only buy 3 cans and that must be customer 50 because all the customers 51-100 must buy more or equal than him for him to be the median.
So now we know how many cans each of them has bought. The median now is between 3 and 4 cans. The average of them is 3,5 cans. So that is the median.
I can say that the median number of 26 28 31 34 37 43 46 49 is 34+37 divided with two, so 71/2 =35,5.
Well good. The median numbers are the one in the middle. When the number of customers are even(100) their must be two values in the middle. We want to get the middle values as high as possible. We have two restrictions though. Everyone must have bought at least 1 can and the total number of can must be 252.
Read the start of my former post to get some more ideas
You are extremely helpful I appreciate.
You´re welcome.
Do you prefer English?
I prefer English and I appreciate Swedish language.
