誤差, 偏差 and 差: identify the reference value
Distinguish a difference from a given true value from a difference from the mean. The same number can express different comparisons depending on its reference.
誤差 compares with a true value
誤差, read ごさ, means error. 測定の誤差を小さくするため同じ作業を繰り返した。 says that someone repeated the same task to reduce measurement error. Repetition alone does not establish that the error actually decreased.
If the given true length is 100 centimeters and the measured length is 102 centimeters, subtracting the true value from the measurement gives an error of plus 2 centimeters. The reference here is the given true value.
偏差 compares with the mean in this example
偏差, read へんさ, means deviation. 各測定値と平均値との偏差を計算した。 says that someone calculated each measurement’s deviation from the mean.
Measurements of 98, 100 and 102 centimeters have a mean of 100 centimeters. The deviation obtained by subtracting that mean from 102 is plus 2 centimeters. The reference here is the mean.
Read the difference and its reference together
差, read さ, means difference or gap. When reading an error or deviation, identify the reference subtracted as well as the size of the difference.
The true value and the mean happen to be 100 in these examples. A mean is not always the true value, so a deviation from the mean is not automatically an error from the true value.
If a measurement is 2 centimeters above the mean, must its error from the true value also be 2 centimeters?
Show the answer and why
No. Deviation from the mean and error from the true value use different references. You need to know the true value separately.