Let the 16 consecutive even numbers be $x, x+2, x+4, \dots, x+30$, where $x$ is the first (smallest) even number.

The average of these numbers is given as 1887. The formula for the average of a set of evenly spaced numbers is the same as the average of the first and last numbers in the sequence.

Thus, we can write the average as:

$\text{Average} = \frac{x + (x + 30)}{2} = 1887$

Simplifying this equation:

$\frac{2x + 30}{2} = 1887$

$2x + 30 = 3774$

$2x = 3774 - 30$

$2x = 3744$

$x = 1872$

So, the first number is $x = 1872$.

The numbers are $1872, 1874, 1876, \dots, 1902$, and the second largest number is the 15th number in the sequence, which is $1900$.

Thus, the second largest number is:

$\boxed{1900}$

Would you like a more detailed explanation or have any questions? Here are five related questions you might explore:

1. How would the formula for the average change if the numbers were odd instead of even?
2. What is the value of the largest number in this sequence?
3. What would the average be if there were 10 consecutive even numbers instead of 16?
4. How can you calculate the sum of these 16 consecutive even numbers?
5. How does the position of a number affect its value in a sequence of consecutive even numbers?

Tip: In sequences of evenly spaced numbers, the average is always the midpoint between the smallest and largest number.