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Measurement is the estimation of the magnitude of some attribute of an object, such as its length or weight, relative to a unit of measurement. Measurement usually involves using a measuring instrument, such as a ruler or scale, which is calibrated to compare the object to some standard, such as a meter or a kilogram. In science, however, where accurate measurement is crucial, a measurement is understood to have three parts: first, the measurement itself, second, the margin of error, and third, the confidence level -- that is, the probability that the actual property of the physical object is within the margin of error. For example, we might measure the length of an object as 2.34 meters plus or minus 0.01 meter, with a 95% level of confidence. Metrology is the scientific study of measurement. In measurement theory, a measurement is an observation that reduces an uncertainty expressed as a quantity. As a verb, measurement is making such observations. It includes the estimation of a physical quantity such as distance, energy, temperature, or time. It could also include such things as assessment of attitudes, values and perception in surveys or the testing of aptitudes of individuals. In the physical sciences, measurement is most commonly thought of as the ratio of some physical quantity to a standard quantity of the same type, thus a measurement of length is the ratio of a physical length to some standard length, such as a standard meter. Measurements are usually given in terms of a real number times a unit of measurement, for example 2.53 meters, but sometimes measurements use complex numbers, as in measurements of electrical impedance.

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