Chemistry · Ch 2 — Introduction to Analytical Chemistry
Precision and accuracy of measurement
Precision and accuracy of measurement
The goal of any measurement is to determine the true (accepted) value of a quantity as closely as possible. Accuracy is defined as how near the measured value comes to that true value — the smaller the error, the greater the accuracy. Accuracy is limited by the sensitivity, or least count, of the measuring instrument, which is simply the smallest quantity that instrument can reliably distinguish. For example, a burette graduated with a least count of 0.1 mL cannot itself tell you anything finer than 0.1 mL, so a reading recorded as 10.2 mL really means that the true value lies somewhere between 10.1 mL and 10.3 mL; this uncertainty is written explicitly as mL. Error in such a measurement can be expressed as absolute error, defined as (observed value − true value), or as relative error, which is generally the more useful quantity because it expresses the absolute error as a percentage of the true value: relative error . Beyond accuracy, chemists are also concerned with precision — how closely repeated measurements of the same quantity agree with one another. Multiple readings of a quantity are taken specifically to reduce the effect of random error; if the readings cluster tightly together, the measurement is said to have high precision, and high precision is a prerequisite for (though it does not by itself guarantee) high accuracy. Precision is expressed through deviation: the absolute deviation of a single reading is the modulus (positive value) of the difference between that reading and the arithmetic mean of the whole set of readings, and it measur …
What this figure shows. The figure illustrates why a measured reading always carries one uncertain digit. A burette graduated with a least count of 0.1 mL is shown with the liquid meniscus in three slightly different positions, (a), (b) and (c), all of which a student would read and record as '10.2 mL' because the meniscus falls close to, but not exactly on, the 10.2 mL graduation mark in each case. The point the figure makes is that the certain part of the reading is '10.' (fixed by the printed graduations the meniscus lies between), while the final digit '2' is an estimate — the true value could plausibly be read as anywhere from about 10.1 mL to 10.3 mL depending on exactly where the eye judges the meniscus to sit relative to the 0.1 mL divisions. This uncertainty is why the reading is written with an explicit error term as mL, the $\ …
Worked out. Absolute error is defined as (observed value − true value), and relative error is the absolute error expressed as a percentage of the true value: relative error = (absolute error / true value) × 100%. Worked example: a 10 g sample of potassium chlorate is decomposed and found to contain 3.8 g of oxygen (the observed value), while the actual/accepted mass of oxygen in that quantity of potassium chlorate is 3.92 g (the true value). Absolute error = observed − true = g; the negative sign shows the experimental result came out lower than the true value. Relative erro …