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Lecture

2a. Terminology.docx

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Department
Chemistry
Course
CHM217H1
Professor
Stone
Semester
Fall

Description
Terminology (3.1-3, 4.1, 5.1-2) (Q3.1-3, 6, 9-13) Range: difference between min and max values Resolution: ability to discriminate between different values (ie. cm, mm, decimal place) Error vs Uncertainty Measurement Error (E): difference between measured (Xm) and true (Xtrue) values • true value should be known • can use conventional or accepted true value (i.e.  = 3.14) Uncertainty (U): our estimate of the likely error in Xm • more realistic to use uncertainty (to it more times) Absolute: Ex = Xm – Xture or ± Ux Relative: Ex’ = – = or U’x = Mean: -Ex when Xm is an average value Standard of Reference for calibration: • determines quality (usefulness) of measurement • determines quality (usefulness) of results Error types Systematic: - all results either too high / low - result in bias - affects accuracy (closeness to true value) are errors that always have the same magnitude and sign, resulting in a bias of the measured values from the true value. An example would be a ruler missing the first 1 mm of its length – it will consistently give lengths that are 1 mm too short. Systematic errors affect the accuracy of the final result. Random: - results fall either side of average - affects precision (spread) of results - express relative to mean or median will have different magnitudes and signs, and result in a spread or dispersion of the measured values from the true value. An example would be any electronic measuring device – random electrical noise within its electronic components will cause the reading to fluctuate, even if the signal it is measuring is completely constant. Random errors affect the precision of the final result; they may also affect accuracy if the number of replicates used is too small. Gross error: irredeemable error resulting in an outlier are errors that are so serious (i.e. large in magnitude) that they cannot be attributed to either systematic or random errors associated with the sample, instrument, or procedure. An example would be writing down a value of 100 when the reading was actually 1.00. If included in calculations, gross errors will tend to affect both accuracy and precision. Precision: describes the reproducibility of a result. If you measure a quantity several times, and the values agree closely with one another, your measurement is precise. If the values vary widely, the measurement is not precise. Accuracy: describes how close a measured value is to the “true” value Replicates What are they? Repeated measurement of the same sample / same parameter / identical conditions Central Value / Central Tendency • arithmetic mean • geometric mean • mean • mode Residuals: ( ) comparison between successive individual values within a set of measurements, show the quality of the data set ∑ Sample mean:
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