Physics · Units And Measurements · NEET
Absolute error tells you the size of the mistake in the same unit as the reading. Example: if length is 5.0 cm and the error is 0.1 cm, the absolute error is 0.1 cm. Relative error compares that mistake to the value itself: 0.1/5.0 = 0.02. So absolute error has a unit (cm), but relative error is just a number with no unit. Relative error tells you how serious the error is compared to the size of the thing you measured.
Yes. Absolute error always has the same unit as the quantity. If you measure time in seconds, the absolute error is in seconds. This is important because relative error and percentage error do NOT have units. NEET options often trick you by giving a unit to percentage error, which is wrong.
In real experiments we never know the exact true value. So we take several readings and use the mean (average) as the best guess for the true value. Mean value a_mean = (a_1 + a_2 + ... + a_n) / n. Then each absolute error is |a_mean - a_i|. The mean of all these absolute errors is called the mean absolute error, and we report the final answer as a_mean plus or minus mean absolute error.
An error of 0.1 cm in 5 cm is small, but the same 0.1 cm in 0.5 cm is large. Dividing by the mean value shows how big the error is compared to the measurement. That is why a small ruler and a long tape can have the same absolute error but very different relative errors. Relative error is the fair way to compare accuracy.
When we report the error of a measurement, we use the size (magnitude) of the error, so it is written as a positive number with a plus-minus sign, like 5.0 cm plus or minus 2%. Individual deviations of single readings from the mean can be positive or negative, but the mean absolute error, relative error and percentage error we report are taken as positive magnitudes.
First find the mean: a_mean = (a_1 + a_2 + ... + a_n)/n. Then each absolute error is delta_a_i = |a_mean - a_i|. Mean absolute error = (delta_a_1 + delta_a_2 + ... + delta_a_n)/n. This mean absolute error is what you plug into relative error = mean absolute error / a_mean, and percentage error = relative error times 100.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Absolute error (size of the mistake, same unit as the quantity), relative error (mean absolute error divided by mean value, no unit), and percentage error (relative error times 100, written as a %).
Relative error is also called fractional error. They mean exactly the same thing: mean absolute error divided by the mean value.
Write it as mean value plus-minus mean absolute error, for example T = 2.62 s plus or minus 0.02 s, or with percentage: T = 2.62 s plus or minus 1%.
When quantities are combined in a formula (added, multiplied, or raised to a power), the errors combine using relative or percentage errors, not absolute errors. So mastering relative error here is the base for the next topics on combination of errors.
In principle yes, if the error is larger than the measured value, but for a careful measurement it is small. NEET questions usually keep percentage errors small (1% to 20%).
