The following joke reads "Be greater than average".
$$ B > \frac{1}{n} \sum\limits_{i=1}^{n}x_i $$
But as a new and n00b mathematician, I find the syntax difficult to understand and I have a question about it.
If the formula for average is$$ Avg = \frac{SumOfTheTerms}{NumberOfTerms} $$
Then I can see how the equation in the joke might be:
$$ \frac{ \sum\limits_{i=1}^{n}x_i }{n} $$
How (or perhaps a better a question would be why) does the $$ \frac{1}{n} $$
get moved to the side of that?
I really appreciate you helping me with my dumb question. Thanks.
$\endgroup$ 81 Answer
$\begingroup$$\frac{1}{n} a = \frac{a}{n} = a \frac{1}{n}.$
Now consider when $a=\sum\limits_{i=1}^{n}x_i.$
$\endgroup$ 1
