# Precision and Accuracy

**Precision :**

The degree of agreement scattered and spread of repeated measurements of the same quantity refers to as Precision. Precision is the degree of agreement among series of measurements of the same physical quantity.

It is a measure of the reproducibility of results rather than their correctness. Good precision means the readings are mostly very close to their mean and is associated with small random errors.

**Accuracy**:

The degree of agreement between the result of a measurement and the true value of the quantity refers to as Accuracy. Accuracy is the degree of agreement between the experimental result and its true value.

Good accuracy means the reading or the mean of a set of readings in very close to the true value, and is associated with small systematic errors.

**Examples:**

A physical quantity m is measured repeatedly. For each recorded m, its frequency of occurence, N is plotted. The true value of the quantity is m.

To deduce the quality of collected data in terms of precision and accuracy, possible results are shown as :

If the measurement is close to the true value it is considered accurate otherwise inaccurate. if repeated measurements are close to each other it is considered precise, otherwise imprecise.

Variables x and y are related by the equation y = p-qx where p and q are constants. Values of x and y are measured experimentally. The results contain a systematic error. Which graph best represents these results?

The answer is **A**

**Comments**: **A **is correct as if shows no random error but a systematic error with the line not going through p. **B** was popular but it shows random error without systematic error.

**Error**

The least unit of measurement is the smallest division available on the

measuring equipment. **The error or uncertainty **is the difference between

the measured value x and the true value and is half the least unit of

measurement (LUM) = Ax, i.e., the measured quantity and its associated

absolute error is therefore written as “x + Ax“ (the absolute error carries

only 1 of 2 sf (significant figures).

**Example: **Given measured gravitational force constant, g = 9.824 + 0.02385 ms ?,the presentation should be

g = 9.82 + 0.03 ms (rounded up to 1 significant figure)

Common mistake in estimating error is by founding down the error to

one significant figure ang presented an such This will reduce the overall

confidence as to whether the final error or uncertainty quoted is all

encompassing of its componential uncertainties,

When this is measured physical quantity is manipulated mathematically with/ out other measures physical quantities, a new derived error has to be assigned based on the following rules.