A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake?

To find the percentage change in the result, we can break down the problem into simple steps by assuming a value for the original number.

Let the original number be $x$.
To make the calculations simple, let us choose $x=4$.

Step 1: Calculate the correct result (expected result)
The number should have been multiplied by 4.
$\text{Correct Result}=4\times 4=16$

Step 2: Calculate the incorrect result (mistaken result)
Instead of multiplying, the number was divided by 4.
$\text{Incorrect Result}=\frac{4}{4}=1$

Step 3: Calculate the change in the result
The absolute change (decrease) in the result due to the mistake is:
$\text{Change}=\text{Correct Result}-\text{Incorrect Result}$
$\text{Change}=16-1=15$

Step 4: Calculate the percentage change
The percentage change is calculated relative to the correct (original expected) result:
$\text{Percentage Change}=\left(\frac{\text{Change}}{\text{Correct Result}}\right)\times 100$
$\text{Percentage Change}=\left(\frac{15}{16}\right)\times 100$
$\text{Percentage Change}=0.9375\times 100=93.75\%$

Thus, the percentage change in the result due to the mistake is 93.75%.