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Mathematics 17 Online
OpenStudy (binary3i):

The average of the numbers is zero tell the range of numbers?

OpenStudy (binary3i):

and they ore positive numbers

OpenStudy (unklerhaukus):

{0}

OpenStudy (anonymous):

The range of a set of numbers is the difference between the greatest and the smallest point of data.

OpenStudy (anonymous):

If the average is 0, then this means that the range is also 0.

OpenStudy (binary3i):

no, there are infinity of those numbers.

OpenStudy (apoorvk):

negative infinity to infinity

OpenStudy (binary3i):

only positive numbers. not even zero.

OpenStudy (binary3i):

any one.

OpenStudy (apoorvk):

how can the average of positive no. be zero??? lol.

Parth (parthkohli):

\(\Large \color{MidnightBlue}{\Rightarrow Mean(average) = {\text{Sum of numbers}\over \text{Number of numbers} } }\)

Parth (parthkohli):

If they are ALL positive, then we can have ONLY a zero.

Parth (parthkohli):

Even if you try it with 1, it'll fail.

OpenStudy (binary3i):

take the sum of infinity GP whose common ratio is 1/x where x is greater than 1. divide the sum with no of terms that is infinity and so the answer comes out to be zero. the common ratio can only be between 0 and one other wise average won't be zero.

OpenStudy (dumbcow):

ahh thus the range is 1 example \[mean = \lim_{n \rightarrow \infty} \frac{\sum_{k=1}^{n}\frac{1}{k}}{n} = 0\]

OpenStudy (binary3i):

range is (0,1)

OpenStudy (dumbcow):

typo, that should be 1/k^2 so that it converges

OpenStudy (binary3i):

i said a GP

OpenStudy (dumbcow):

oh oops

OpenStudy (binary3i):

\[(\sum_{r=1}^{n}1/(x^r))/n\]

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