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?

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- Aug 23rd 2010, 12:13 AMrai2003Mean 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 AMspycrab
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:

$\displaystyle (7*20)-69=71$

Answer: 71

verify:$\displaystyle \frac{1+2+3+20+21+22+71}{7} = 120$ (120 is max value for equation, calculate by $\displaystyle 7*20$ - Aug 23rd 2010, 05:04 PMrai2003
thanks