Can someone explain how to work this?

Question

The average of 16 consecutive multiplies of 4 is 26. What is the median of these numbers?

The answer is -1 and I don't see how they got that.

Answer 1

i can show you where i think they get -1, but I don't think that is the correct answer to the problem as stated

the statement of the problem is that the average of 16 consecutive numbers is 26...meaning if we figure out which numbers to add, we should add those 16 numbers and their average will be 26

the numbers are multiples of 4; that means we can write the first one as 4n...the next one is 4(n+1), the next one is 4(n+2) and so on

adding these gives us:

[4n+4(n+1)+4(n+2)+...4(n+14)+4(n+15)]

=4[n+n+1+n+2+n+3...=4[16n+120]

this is the sum of those numbers

the average is the sum divided by 16 and we have

4[16n+120]/16=26

solving

n= -1

but, this means that the first number in the sequence is 4x(-1)=-4...and the 16 numbers in the sequence are:

-4,0,4,8,12,16,20,24,28,32,36,40,44,48...

and the median of these numbers is 26, since when you have an even number of items in a sequence, the median is the arithmetic mean of the two central numbers (in this case the mean of the 8th and 9th numbers, 24 and 28)

hope this helps

Answer 2

I don't see it either.  The median of these numbers should be exactly the same as the mean, since they are evenly distributed.

Specifically, the number must be

-4, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56

These are the only 16 consecutive multiples of 4 with mean 26, and the median is by definition the average of 24 and 28.