Which experimental error by taking repeated
measurements is called a systematic error?
Here are the steps to calculate experimental error by taking repeated measurements:
1. Perform the experiment and collect a set of repeated measurements for the same quantity or parameter.
2. Calculate the average value of the measurements by adding up all the values and dividing by the total number of measurements. Let's call this average value "X_avg."
3. Calculate the deviation of each measurement from the average value by subtracting the average value from each measurement. Let's call this deviation "ΔX."
- For each measurement, subtract X_avg from the value obtained: ΔX1 = X1 - X_avg, ΔX2 = X2 - X_avg, ΔX3 = X3 - X_avg, and so on.
4. Square each deviation to get the squared deviation, ΔX^2.
- For each deviation, square the value obtained: ΔX1^2, ΔX2^2, ΔX3^2, and so on.
5. Calculate the sum of the squared deviations, Σ(ΔX^2).
- Add up all the squared deviations to get the sum: Σ(ΔX1^2 + ΔX2^2 + ΔX3^2 + ...).
6. Divide the sum of squared deviations by the total number of measurements minus one to get the mean squared deviation, MSE.
- MSE = Σ(ΔX^2) / (N - 1), where N is the total number of measurements.
7. Calculate the experimental error from the mean squared deviation using the formula:
- Experimental error = square root of (MSE).
By following these steps, you can determine the experimental error based on repeated measurements.