Let's solve the expression step by step:

Expression:

$\left(\frac{{10,000 - 13,000}}{{\left(\frac{{10,000 + 13,000}}{2}\right)}}\right) \times 100$

Step 1: Calculate $10,000 - 13,000$

$10,000 - 13,000 = -3,000$

Step 2: Calculate $10,000 + 13,000$

$10,000 + 13,000 = 23,000$

Step 3: Calculate the average $\frac{23,000}{2}$

$\frac{23,000}{2} = 11,500$

Step 4: Divide the result from Step 1 by the result from Step 3

$\frac{-3,000}{11,500} \approx -0.26087$

Step 5: Multiply by 100 to get the final result

$-0.26087 \times 100 = -26.087$

So, the final result is approximately: $\boxed{-26.087}$

Would you like more details or have any questions?

Here are 8 related questions:

1. What is the significance of using the average in this formula?
2. How would the result change if the values of 10,000 and 13,000 were swapped?
3. Can you apply this formula to different numbers?
4. What does a negative result indicate in this context?
5. How would this formula apply to real-world financial analysis?
6. What if both numbers were equal? What would be the result?
7. Can you explain the formula in the context of percentage change?
8. How is this formula related to the concept of relative change?

Tip: Always check the units of measurement when applying mathematical formulas to ensure consistency and accuracy.