SOLUTION: The mean of the eight positive intergers (all < 10) 5,8,X,X,6,Y,6,5 is 7. Find the values of X and Y, and then state the median of the intergers.

Algebra ->  Probability-and-statistics -> SOLUTION: The mean of the eight positive intergers (all < 10) 5,8,X,X,6,Y,6,5 is 7. Find the values of X and Y, and then state the median of the intergers.       Log On


   

Question 1020446: The mean of the eight positive intergers (all < 10) 5,8,X,X,6,Y,6,5 is 7. Find the values of X and Y, and then state the median of the intergers.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
7 being the mean of the eight numbers means that
%285%2B8%2Bx%2Bx%2B6%2By%2B6%2B5%29%2F8+=+%2830%2B2x%2By%29%2F8+=+7
==> 30+2x+y = 56
==> 2x+y = 26
Only two positive integers both less than 10 will satisfy the last equation, namely highlight%28x+=+9%29 and highlight%28y+=+8%29.
Now that x and y are known, arrange the positive integers in an array:
5,5,6,6,8,8,9,9
The median of the data set will be the average of the two middle terms 6 and 8, namely highlight%287%29.