Average of 5 Numbers Equals 7: Testing Number Inclusion Properties

To solve this problem, we should understand what it means when the average of five numbers is 7. The average is calculated by taking the sum of the numbers and dividing by the number of numbers. Given that the average is $7$, the equation can be written as:

$\frac{a + b + c + d + e}{5} = 7$

Multiplying both sides by $5$ gives:

$a + b + c + d + e = 35$

This equation tells us that the sum of the numbers $a, b, c, d, e$ is $35$. Now, we address whether at least one of these numbers must be $7$.

Consider the set of numbers $a = 1$, $b = 1$, $c = 1$, $d = 1$, and $e = 31$. The sum of these numbers is:

$1 + 1 + 1 + 1 + 31 = 35$

The average is:

$\frac{35}{5} = 7$

Here, none of the numbers are $7$, yet the average is still $7$. This example shows that it is not necessary for any of the numbers to be $7$ for the average to be $7$.

Therefore, the conclusion is that the number $7$ is not necessarily one of the numbers.

Thus, the correct choice is : No.