Error analysis

For a product, quotient or power, add the percentage errors, each multiplied by its power. If Z = A³ B / C², then ΔZ/Z = 3 ΔA/A + ΔB/B + 2 ΔC/C. For a sum or difference add the absolute errors: ΔZ = ΔA + ΔB.

The error shown is the largest possible one. In the worst case each measurement is off in the direction that pushes the result the same way, so the errors pile up.

Take the mean of the readings. The absolute error of each reading is its distance from the mean. The mean absolute error is the average of those distances, and the result is written as mean ± mean absolute error. For 2.63, 2.56, 2.42, 2.71 and 2.80 s it is 2.62 ± 0.11 s, a percentage error of 4%.

It is the smallest value an instrument can read. For a vernier callipers it is 1 main scale division divided by the number of vernier divisions. For a screw gauge it is the pitch divided by the number of circular scale divisions.

Absolute error is the size of the error in the unit of the quantity. Relative error is the absolute error divided by the value. Percentage error is the relative error times 100.

A percentage error says how big the error is compared with the value, and a sum mixes values together. To add the errors of a sum you need the actual values, as in the equivalent resistance of two resistors in parallel: 100 ± 3 ohm and 200 ± 4 ohm give 66.7 ± 1.8 ohm.