refers to the difference between a measured value and the “true” or “known” value.

a sample of about the same size that is carried through an analysis in exactly the same way.

The most widely used measure of central value is the

is the middle value in a set of data that has been arranged in numerical order

a result that differs significantly from others in the set.

can have a significant effect on the mean of the set but has no effect on the median.

is the closeness of results to others obtained in exactly the same way

describes the reproducibility of measurements—in other words, the closeness of results that have been obtained in exactly the same way.

indicates the closeness of the measurement to the true or accepted value and is expressed by the error.

describes the agreement among several results obtained in the same way

often more difficult to determine because the true value is usually unknown.

E in the measurement of a quantity xi is given by the equation

is the difference between the measured value and the true value.

is the absolute error divided by the true value.

is often a more useful quantity than the absolute error. The percent relative error is given by the expression

causes data to be scattered more or less symmetrically around a mean value

causes the mean of a data set to differ from the accepted value.

They usually occur only occasionally, are often large, and may cause a result to be either high or low. They are often the product of human errors.

They arise from experimental variables that cannot be controlled or determined.

These errors often occur when instruments or measuring devices are uncalibrated or are calibrated improperly. They have the same effect on all samples.

The substance being determined is called the a

occur infrequently and often result from an experimental blunder such as misreading a scale or interpreting a number incorrectly

an occasional result in replicate measurements that differs significantly from the other results.

measures the systematic error associated with an analysis. It has a negative sign if it causes the results to be low and a positive sign otherwise.

are caused by nonideal instrument behavior, by faulty calibrations, or by use under inappropriate conditions

arise from non ideal chemical or physical behavior of analytical systems.

result from the carelessness, inattention, or personal limitations of the experimenter.

eliminates most systematic errors of this type.

are independent of the size of the sample being analyzed.

decrease or increase in proportion to the size of the sample.

are substances sold by the National Institute of Standards and Technology (NIST) and certified to contain specified concentrations of one or more analytes.

contains the solvent and all the reagents in an analysis.

refers to the collection of all the constituents in the sample.

contains the reagents and solvents used in a determination but no analyte

a bell-shaped curve

a set of replicate measurements is the difference between the highest and lowest result.

directly from an accumulation of all random uncertainties in the experiment.

a bar graph

occurs for a series of discrete events where the average time between events is known, but the exact timing is random.

materials that contain one or more analytes at known concentration levels.

the collection of all measurements of interest to the experimenter

a subset of measurements selected from the population.

refers to an estimate of a parameter that is made from a sample of data as discussed next

refers to quantities such as m and s that define a population or distribution.

the arithmetic average of a limited sample drawn from a population of data

a measure of the precision of the population, is given by summing the squares of the deviations from the mean

It is an estimate of the population variance 

is the standard deviation of a set of data divided by the square root of the number of data points in the set.

another term that is sometimes used to describe the precision of a set of replicate results

is the range of values within which the population mean is expected to lie with a certain probability.