Measures play an important role in everyone’s life, whether at a medical checkup, during a sports competition or when building a house. In Power BI, a Measure is a numeric column (not columns participating in relationships) that by default is set to be automatically summarizable in all visuals.

A bartender pours a large measure of whiskey into the glass.

## Definition

Measures are a fundamental concept in mathematics. They form the basis of many concepts in analysis and probability, including s-algebras and integrals. The study of measures is known as measure theory.

In mathematical terms, a measure is a set function that assigns each pair of sets in a collection a value. Typically, the value has the properties of sigma finiteness and finite additivity.

If all these conditions are satisfied, the collection is called a measure space and the members are called measurable sets. The simplest measure is a countable measure, which is a complete translation-invariant measure on R

## Purpose

Measures allow you to create aggregates such as sums or averages. They are usually used to represent business-specific quantities such as sales, website visits or customer calls. Measures differ from calculated columns in that they do not use data stored in the data model (which increases the size of your model and consumes RAM). In addition, a measure can be evaluated within the filter context of the visual in which it is applied, while a calculated column formula is only evaluated once when you first define them or when you refresh your dataset.

A measure’s validity is determined by various types of evidence, such as whether it covers the construct it is supposed to and if the scores produced by the measure are correlated with variables that are expected to be correlated. You can test the reliability of a measure by conducting a series of studies using it.

## Accuracy

Accuracy describes how close measurement results are to a true value. It includes both random and systematic error.

Precision indicates how close the values of multiple measurements in a series are to each other. This is independent of accuracy. You can have high precision without being accurate, or low precision with high accuracy.

Gage R&R studies (repeatability and reproducibility) determine the precision of a measuring process over time, with and without different devices and personnel. This allows you to determine the sources of variability and correct them. If your project measurements are off target on average, you can run gage R&R studies to pinpoint the problem. This is the first step to improving your accuracy. It also helps you quantify how much improvement is needed.

## Units

Units of measurement are the standardized quantities that are used to define physical properties. They are a central part of the scientific method because they ensure that results can be reproduced.

There are many different units of measure, but the most common are length, time, mass and volume/capacity. They play an important role in math education, teaching children how to add and subtract and compare different lengths, volumes/capacity and more.

There are several different systems of measurement, but the most commonly used is the metric system, which is internationally regulated by the International Bureau of Weights and Measures (BIPM). This standard includes decimalization, a system of prefixes, and seven base units from which all other physical quantities can be derived. These base units are also called fundamental units or invariant units.

## Uncertainty

The results of any measurement may be affected by the accuracy of the measurement system used, the environment, the skill of the operator and many other factors. Uncertainty values are calculated to describe these effects. They are often stated in the form of a range or interval with a given level of confidence.

In other words, the uncertainty describes the probability that a measurement will lie within a specified interval around the measured value. A commonly quoted uncertainty is a value plus or minus one standard deviation (SD). Other terms that are sometimes used include coefficient of variation (CV) and confidence intervals. These should always be clearly understood before using them. This is especially important when communicating about measurements to other scientists. A good source of further information is the ISO Guide to the Expression of Uncertainty in Measurement.