margin of error : a value that tells us the error or uncertainty connected with a number, such together a measurement.

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indirect measure up : a measurement that requires estimating an unknown value by measure something that is known.

Measurement affects numerous different elements of our lives. Ours admittance to college counts on qualities – the measure of our performance in various classes; us assess phone to plan by exactly how much data usage they allow; us count calories and also our physicians look to see that our blood sugar and also cholesterol levels space safe. In almost every page of contemporary life, values – measurements – play an essential role.

From the earliest documented days in ancient Egypt (see number 1), solution of measure up have enabled us come weigh and also count objects, delineate boundaries, note time, create currencies, and describe herbal phenomena. Yet, measurement comes with its own collection of challenges. From person error and accidents in measuring to variability to the merely unknowable, even the most an exact measures come v some margin that error.

Figure 1: one Egyptian ceremonial cubit pole in the Louvre Museum. The cubit to be a standard straight measurement in old Egypt.image © Uriah Welcome

Early history of measurement

Archeological artifacts show us that systems of measurement date ago before 2500 BCE – over 4,500 years ago. As old civilizations in components of the world as disparate as Greece, China, and Egypt became more formalized, the acts of splitting up floor or trade through others brought about a require for standardizing approaches for measure things. Since measurement is greatly a issue of to compare of one point to another, it isn’t surprising that early systems often started with objects the were usual to the community. The load of one grain of wheat, for example, or the 3) or milliliters (ml).">volume of fluid that might be held by one goat skin were used as standards.

Interestingly, plenty of of these solution initiated v the person body. For example, the Egyptian "cubit" was assessed as the length of a male forearm indigenous the tip of the middle finger to the elbow (roughly 48 cm, or 19 in). In India’s Mauryan period (500 BCE), 1 "angul" to be the broad of a finger (roughly 1 cm, or 0.4 in). The ancient Greeks and Romans supplied the units "pous" and "pes," both of which translate into "foot." Unsurprisingly, this measure was based on the size of a masculine foot indigenous the big toe come the hoe (roughly 29.5 cm, or 11.6 in).

However, as any trip to a clothing or shoe store will show, not all bodies room the same. As soon as measuring something small, prefer a table, the difference between one masculine foot and also another’s can not make lot difference. However, if what is gift measured is much larger – say, a plot of land – those little differences add up (a magnification error that we’ll talk about shortly). In an effort to it is in fair to every its citizens, many worlds moved to standardize measurements further. By 2500 BCE, the “royal cubit” in Egypt was figured out by the forearm size of the Pharaoh and also carved right into black marble. It was about 52 centimeter in size (20.5 in) and also was further divided into 28 same segments, approximating the width of a finger. This noted a baseline because that others and consistency throughout the kingdom. People could carry a rod or various other object that might be marked, put it against the marble and, in effect, create a leader that they might use to measure length, width, or elevation elsewhere.

As civilizations progressed and dimensions became much more standardized, solution of measure up were occurred with boosting complexity. The ancient Mesopotamians were among the first to measure angles and also time, separating the course of the sun on the celestial sphere into twelve 30-degree intervals (1/360 the the one of the circle, number 2). They likewise used the brand-new crescent step of the moon to mark the begin of a new month. Celestial objects like the Sun and also stars were provided to monitor hours, through the usage of sundials or the known seasonal positions of stars. Measurement has actually a long and complex history.

Figure 2: A part of the Sumerian polite calendar indigenous the city that Nippur. Using huge cycles, the calendar divides a month right into 30 work of 12 city hall (equal to 2 hours) and 1 year right into 12 months of 30 days. Both systems an outcome in the circumference of a circle: 360 degrees.image © Lamassu architecture

Measurement: standardized numbers and also units

Measurement offers us a method to communicate with one another and also interact v our next site – however it only works if those you are interacting with understand the solution of measure up you room using. Imagine you open up a recipe book and also read the following:

Mix white street (10) through flour (1) and also water (100). Wait for 1, and also then bake because that 1.

How would you go around using this recipe? exactly how much sugar perform you use? 10 grams? 10 teaspoons? 10 pounds? how much flour or water? cups? liters? Milliliters? how long perform you wait? Minutes? Hours?

All measurement entails two parameters: the amount existing (i.e., the number) and the unit within a mechanism of measurement. The cooking recipes lists the amounts (1, 10, and also 100), but not the units. There is no both parameters, the info is basically useless. (To see a cooking recipes with quantities and units, see figure 3.)

Figure 3: A handwritten recipe for sweet potato & zucchini bread.image © Charles Willgren, Flickr

There are numerous different solution of measurement devices in the world, yet one generally used in scientific research is the metric system (described in more detail in our Metric mechanism module). The metric device uses very an exact base standards, such as the meter, a unit of length, i m sorry is defined as "the length of the path travelled by irradiate in a vacuum during a time expression of 1/299,792,458 the a second."

Figure 4: an example of a food label.image © BruceBlaus

How carry out we measure? direct versus indirect measurement

The question of how come measure has actually been the topic of an excellent discussion since antiquity. Countless of the solution of measure debated in the previous ar relate come direct measurement. Direct measurement offers us a an extremely clear, quantifiable value of "this-equals-that." I have the right to count the variety of minutes or hours until mine summer vacation, or the variety of miles between my house and also my favorite restaurant. But some amounts are no so easily measured. While friend might be able to use a ruler to measure the dimensions of her bedroom, or also the distance to a neighbor’s house, girlfriend can’t simply use a lengthy ruler to measure the depth of the ocean.

In instances like these, researchers are referred to as upon come make measurements that are complicated or difficult to do in a straight way. Thus, indirect dimensions are typically used in scientific research to determine values because that properties that cannot it is in measured directly. Indirect measurement involves estimating one unknown worth by measure up something the is known. For example, the nationwide Oceanic and Atmospheric management (NOAA) that the United claims government generally relies on sonar-based dimensions to produce maps of s depth. This an approach involves sending out out sound waves into the water and then measure up the amount of time the takes for the sound to be reflected ago to the instrument. Due to the fact that the rate of sound is known, by measure the time between the initial transmission and reception of the response, a sonar operator can calculate the distance to the object, and also thus the depth of the s (Figure 5).

Figure 5: establishments like NOAA usage sound waves (sonar) to identify the depth the the water (in this image, the depth is represented by color) and also to determine objects.image © MingTsang Lin

Measurement error

Science has, over time, built a reputation as being objective, careful, and precise – or, in ~ least, as specific as is possible given the recent knowledge and technology. This leads many to believe that as soon as errors in science happen they space the an outcome of human error. When mistakes absolutely do happen, the "error" in measurement error go not median a mistake has actually taken place, it refers to the variability about a particular measurement.

Figure 6: depictions of error propagation in an iterative, dynamic system. ~ ~1,000 iterations, the error is tantamount to the worth of the measurement itself (~0.6) do the calculation fluctuate wildly. Adjusted from IMO (2007).


We are constantly measure up the world roughly us and also using that information to do decisions. Indigenous the casual decision on the kind of snack to enjoy to the crucial one of how much medication to take, us quantify and measure values. And also we’ve been measuring the human being since very early times, make adjustments and brand-new discoveries of just how to measure continuously. With all of these measurements there is a margin the error included in also the most an accurate measurement. However through awareness of this errors and also careful fist to the values and units, we have the right to approach an extremely high level of accuracy in ours measurements. And that is the ultimate score of measure up – to administer accurate details that everyone deserve to understand and use.


In nearly every facet of contemporary life, values – dimensions – play critical role. Us count calories for a diet, stores measure the percent of taxation on our purchases, and also our medical professionals measure important physiological indicators, choose heart rate and also blood pressure. Native the earliest documented days in ancient Egypt, systems of measure have enabled us come weigh and also count objects, delineate boundaries, mark time, develop currencies, and also describe herbal phenomena. Yet, measure comes v its own series of challenges. From person error and accidents in measuring to variability come the simply unknowable, even the most specific measures come v some margin that error.

Key Concepts

Since your earliest days, equipment of measure up have noted a common ground for individuals to describe and understand their world. Measurement help to provide context come observations and a method to explain phenomena.

A measurement consists of two parts – the amount existing or numeric measure, and also the unit that the measurement represents in ~ a standardized system.

When straight measurement is not possible, scientists can estimate parameters v indirect measurement.

While errors do take place in measurement, measure error typically refers come the apprehension or variability around a measure the occurs naturally as result of the restrictions of the tool we are using to measure up the quantity.

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additional Reading

Heather MacNeill Falconer, M.A./M.S., Anthony Carpi, Ph.D. “Measurement” Vol. MAT-3 (8), 2017.