Re: Set H contains five positive integers such that the mean, median, mod
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09 Sep 2022, 07:32
Set H contains five positive integers such that the mean, median, mode, and range are all equal. The sum of the data is 25.
sum=25 of 5 positive integers so we know mean = 5 that means median mode range are also all equal to 5.
mode=5 means 5 is most repeated so we have atleast 2 5's
For the median to be 5, with two 5s, there must be at least one number above 5
The sum of remaining 3 numbers would atmax be x+y+z= 15 ( 25-10, 2 5s for 5 to be the mode)
x,y,z are the remaining numbers and distinct values( if there are 2 5's only we will know that later) lets assume x>y>z
for range to be 5, x=z+5
2z+y+5=15
2z+y=10
if y=z, then y=3 (rounded off) so z<3.5 so possible values for z,y,x= {1,8,6},{2,6,7},{3,4,8}
we know x>y>z that is only possible in the 2nd and 3rd combination so we get
2,5,5,6,7 or 3,4,5,5,8
the smallest possible number is either 2 or 3 and both of them are less than quantity B so
Quantity B is greater