Enter the actual value and the approximate value into the calculator to determine the midpoint error. The midpoint error is a measure of the relative error between the actual and approximate values, expressed as a percentage.
Midpoint Error Formula
The following formula is used to calculate the midpoint error:
E_m = left| frac{V_a - V_p}{frac{V_a + V_p}{2}} right| times 100%
Variables:
- Em is the midpoint error (%)
- Va is the actual value
- Vp is the approximate value
To calculate the midpoint error, subtract the approximate value from the actual value, divide by the average of the actual and approximate values, take the absolute value, and then multiply by 100 to get the percentage.
What is Midpoint Error?
Midpoint error is a type of relative error that provides a measure of the accuracy of an approximation compared to the actual value. It is particularly useful when the actual value and the approximate value are both positive and of similar magnitude. The midpoint error is expressed as a percentage, which allows for an easy comparison of the accuracy of different approximations.
How to Calculate Midpoint Error?
The following steps outline how to calculate the Midpoint Error:
- First, determine the actual value (Va).
- Next, determine the approximate value (Vp).
- Use the formula Em = |(Va – Vp) / ((Va + Vp) / 2)| × 100% to calculate the midpoint error.
- Finally, calculate the Midpoint Error (Em) as a percentage.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Actual value (Va) = 100
Approximate value (Vp) = 95
