Table of Contents

## An Introduction to Measurements

Precision in Math: A measurement is a numerical value that is assigned to a physical quantity. The measurement can be used to compare two or more physical quantities, or to quantify a change in a physical quantity. There are a variety of units that can be used to measure physical quantities, depending on the type of quantity being measured.

- Some common units of measurement include the meter for length, the kilogram for mass, and the second for time. There are also a variety of units that can be used to measure temperature, such as degrees Celsius and Fahrenheit. When measuring a physical quantity, it is important to use the correct unit of measurement.
- One of the most important things to understand about measurements is that they are always approximate. This is because no physical quantity can be measured with absolute precision. For example, when measuring the length of a room, it is impossible to determine the exact length with absolute precision. There will always be some uncertainty in the measurement.
- This uncertainty can be expressed as a margin of error. The margin of error is a measure of the uncertainty in a measurement. It is usually expressed as a percentage of the measurement. For example, if the margin of error in a measurement is 5%, then the uncertainty in the measurement is 5%.
- When using measurements to compare two or more physical quantities, it is important to consider the margin of error. If the margin of error is too large, then the comparison may not be meaningful.

## Precision – Concepts of Accuracy and Precision

Accuracy is the degree of conformity of a measurement to the true value of the measurand. Precision is the degree of repeatability of a measurement.

### The Concepts of Precision and Accuracy are Easily Confused. But is Possible to Differentiate it after Understanding the Following Explanations

Precision is the closeness of a set of measurements to one another. Accuracy is how close the measurements are to the true value.

## Formula For Precision

Precision is a measure of how close a set of measurements are to each other. The formula for calculating precision is:

- Precision = (Standard Deviation of Measurements) / (Average of Measurements)

## Precision is Often Separated into Repeatability and Reproducibility

- Repeatability is the ability of a measurement system to produce the same results when measurements are repeated under the same conditions.
- Reproducibility is the ability of a measurement system to produce the same results when measurements are repeated under different conditions.