Relative error refers to the error caused by measurementabsolute errorAndMeasured(Agreed)The value obtained by multiplying the ratio of true value by 100%percentageexpress.Generally speaking, the relative error can better reflect the credibility of the measurement.Let the measurement result y minus the measured agreed true value t, and the error or absolute error obtained is Δ.The relative error can be obtained by dividing the absolute error Δ by the agreed true value t.
Relative error=absolute error ÷ true value.Is the ratio of absolute error to true value(It can be expressed in percentage, thousandth and millionth, but it is often expressed in percentage)。Generally speaking, the relative error can better reflect the credibility of the measurement.
Relative error refers to the value obtained by multiplying the ratio of absolute error caused by measurement and measured (agreed) true value by 100%, expressed in percentage.Generally speaking, the relative error can better reflect the credibility of the measurement.Let the measurement result y minus the measured agreed true value t, and the error or absolute error obtained is Δ.Divide the absolute error Δ by the agreed true value t to obtain the relative error
classification
Announce
edit
Absolute error indicates both the size of the error and its positive and negative directions, and is reflected in the same unit dimensionmeasurement result The value that deviates from the true value, which exactly represents the actual size of the deviation from the true value.
Relative error refers to "the ratio of the absolute error of measurement to the true value of measurement", that is, the error is equivalent to the percentage of the absolute error of measurement in the true value (or given value) or expressed in order of magnitude. It is a dimensionless value.Some measuring instruments are determined according to the actual use needsAccuracyorAllowable error, often expressed by quotation error and decibel error.
Reference error refers to the ratio of absolute error to a specific value (upper limit of measuring range or measuring range). The value is expressed in percentage, which is another expression of relative error.
Decibel error is an expression of relative error often used in measuring instruments such as radio and acoustics.To sum up, the above is the category of relative error:
① Actual relative error;
② Relative error of given value;
③ Citation error;
④ Decibel error.
formula
Announce
edit
(δ - actual relative error, generally given in percentage, △ - absolute error, L - measured actual value[2] )
OneApproximate numberAnd itExact numberThe absolute value of the difference is called the absolute error of the approximation.Use a to represent the approximate number, and A to represent its exact number. Then the relative error of the approximate number a is | a-A |/A.
In addition, since the true value of the measured value is unknown, its relative error cannot be accurately known. When we refer to the relative error, we generally meanRelative error limit, that is, the possible relative errorMaximum(upper limit).
Measured valueOfmeasurement errorThe ratio of the absolute value of to the corresponding measured value.bydimensionA quantity of one, usually expressed as a fraction with a molecule of 1, often used to describeLinear quantityPrecision of.When describing the accuracy of linear quantity (length or physical quantity only related to length, such as length, area, volume, etc.), it is necessary to consider not only the error of linear quantity, but also the size of linear quantity itself.
For example, when a surveyor uses the same ruler to measure an object with a length of 1 cm and 10 cm, the absolute error of their measured values is obviously the same, but the relative error of the former is an order of magnitude larger than the latter, indicating that the measured values of the latter are more reliable.
Refers to the absolute error withinTrue valuePercentage in[1]。
