# Mean and median.

• Aug 23rd 2010, 12:13 AM
rai2003
Mean and median.
A set of seven different positive intergers has mean and median both equal to 20. what is the largest possible value this set can contain?
• Aug 23rd 2010, 05:47 AM
spycrab
Quote:

Originally Posted by rai2003
A set of seven different positive intergers has mean and median both equal to 20. what is the largest possible value this set can contain?

You know what the 4th value has to be 20.
So you have __,__,__,20,__,__,__
Fill the first 3 numbers with the smallest 3 positive integers (1,2,3)
now you have 1,2,3,20,__,__,__
fill the next to numbers after 20 with 21 and 22
1,2,3,20,21,22,x
Since the average formula is $\displaystyle \frac{sum of elements}{number of elements}$,
put what you know into the formula:$\displaystyle \frac{69+x}{7}$
Calculate the maximum value by multiplying 7 by 20 and subtracting 69:
$\displaystyle (7*20)-69=71$
verify:$\displaystyle \frac{1+2+3+20+21+22+71}{7} = 120$ (120 is max value for equation, calculate by $\displaystyle 7*20$