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# What is the mean and the median of 7 consective integers the

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Manager
Joined: 28 Apr 2003
Posts: 95
Location: Singapore
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What is the mean and the median of 7 consective integers the [#permalink]  09 Dec 2003, 04:39
What is the mean and the median of 7 consective integers the least of which is x?

I wondering if anyone can have a simpler method to get x+3

x+x+1+x+2.......x+6 x+3
------------------------ =
7
SVP
Joined: 03 Feb 2003
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consequtive integers, or evenly spaced has a one feature
mean=median

x
x+1
x+2
x+3
x+4
x+5
x+6

the median is x+3
the mean is [7x+21]/7=x+3
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
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if you add seven consecutive integers from 0 to n then
their sum s = n(n+1)/2
We have seven consecutive integers ranging from x+0 to x+6
s = 6 * ( 6+1 ) / 2 = 21
We are also adding x seven times
so we have total = 7x+21
average = (7x+21 )/7 = x+3

Median = average if we have odd numbers
Median = average of middle two numbers if we have even numbers.

In this case the Median = x+3
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
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Here's how I did it.

For now, don't worry about the x. Focus on "7 consecutive integers from x" part.
Since you know that median of 0 to 6 is 3 and the average is also 3, you can use this information with x included in there. All you have to do is add 3 to x. Which ultimately is the answer.
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