longhaul123 wrote:
can someone please assist me with this question
Since the question is stating that there are 5 groups of 9 terms each the 5th value of the group is the median.
therefore the actual median for 5 groups are G1- 5
G2 -14
G3=23
G4=32
G5=41
these are the actual median and the actual average of these median is 23
Now from here what is the next possible step ??Can someone Assist
hello pal,
The question asks you the maximum possible value. Surely the answer you arrived at is a possible avg of the medians of the gr,oup. But it is not the maximum avg.
Whenever you are asked to maximize something you have to minimize other elements as much as possible.
Median of a set is derived by arranging the set in ascending order and then if the number of elements in the set is odd then the middle term is the median. Here as each group is divided in 9 elements therefore the median is the 5th element. So far so good.
Now we have to maximize. >> we have all distinct numbers. Note that itis not mandatory that we choose the element sequentially. We just have to arrange the elements of the set in ascending order.
So to maximize start from the greatest number. As we have to arrange in ascending order , the largest will come at the last >> (...,41,42,43,44,45) now AS WE HAVE TO MAXIMIZE DO NOT WASTE THE LARGER NUMBERS. USE THE SMALLER NUMBERS BEFORE THE MEDIAN>> ( 1,2,3,4,41,42,43,44,45). This is 1st set with median 41.
Now remember th,at elements can be used only once>> we have used up the above set so start again from the unused largest ,number>> (...,36,37,38,39,40) and now choose the lowest of the remaining >> (5,6,7,8,36,37,38,39,40)>> median 36.
similarly you get M3=31 M4=26 M5=21.
avg= (41+36+31+26+21)/5 = 31 E