What is $\cfrac 1n$ in this expression? 
I bought a T-shirt at Kenendy Space Center a while back that had this expression on it:
$$
B > \frac1n\sum_{i=1}^n x_i
$$

And below it is captioned "Be greater than average."
I can see the "Be greater than" and the "average" in the expression, but I do not understand what the $\cfrac 1n$ is for.

So, what is the purpose of $\cfrac 1n$ in the expression above?

(Sorry, I have absolutely no idea how to tag this)

The term $\dfrac 1n$ is part of the average. If we want to find the average of two numbers $a$ and $b$, the average would be $\dfrac{a + b}{2} = \dfrac 12(a + b)$. The denominator is equal to the amount of variables we have. In this case, we have two variables $a$ and $b$, so we add them together and divide it by two. This means that the average of $a, b$ and $c$ is equal to $\dfrac{a + b + c}{3} = \dfrac 13(a + b + c)$. The average is also known as the arithmetic mean, and the right hand side of the inequality is just notation for the average of $n$ given variables denoted as $x_i$.

$$\sum_{i=1}^n x_i$$ is read as the sum that goes from $x_1$ to $x_n$. In other words, it is the sum that takes the values of $x_i$ from $i = 1$ to $i = n$. We can now write this as $$\sum_{i=1}^n x_i = x_1 + x_2 +\cdots + x_n$$ and now to find the average of these $n$ different variables, we divide by the total of how many there are, which is $n$. This is the same as multiplying the entire sum by $\dfrac 1n$ which makes the right hand side of the inequality define the average of $n$ variables. Now it is clear that the symbols $$B > \frac 1n \sum_{i=1}^n x_i$$ means be greater than the average.
