Presentation on theme: "Accuracy is the closeness of a measured value to the true value."— Presentation transcript:
1Accuracy is the closeness of a measured value to the true value. For example, the measured density of water has become more accurate with improved experimental design, technique, and equipment.Density of H2O at 20° C(g/cm3)11.01.000.9980.9982
2ACCURACYPercent error is used to estimate the accuracy of a measurement.Percent error will always be a positive.What is the percent error if the measured density of titanium (Ti) is 4.45 g/cm3 and the accepted density of Ti is 4.50 g/cm3?
3Measured Concentration PRECISIONPrecision is the agreement between repeated measurements of the same sample. Precision is usually expressed as a standard deviation.For example, the precision of a method for measuring arsenic (As) was determined by measuring 7 different solutions each containing 14.3 μg/L of As.Measured Concentration(μg/L)18.413.614.216.017.8Average = 15.3 μg/LStandard Deviation = 2.1 μg/LWhat is the true concentration of As in this experiment?Estimate the accuracy of this method.How precise is this method?14.3 μg/L2.1 μg/L
4ACCURACY AND PRECISION Describe the accuracy and precision of these 4 targets.Accurate, and precisePrecise, but not accurateAccurate, but not preciseNot accurate, and not precise
5ERRORSSystematic (or determinate) errors are reproducible and cause a bias in the same direction for each measurement.For example, a poorly trained operator that consistently makes the same mistake will cause systematic error. Systematic error can be corrected.Random (or indeterminate) errors are caused by the natural uncertainty that occurs with any measurement.Random errors obey the laws of probability. That is, random error might cause a value to be over predicted during its first measurement and under predicted during its second measurement. Random error cannot be corrected.
6INTERPOLATION AND SIGNIFICANT FIGURES By convention, a measurement is recorded by writing all exactly known numbers and 1 number which is uncertain, together with a unit label.All numbers written in this way, including the uncertain digit, are called significant figures.For example, the blue line is 2.73 cm long. This measurement has 3 significant figures. The first 2 digits (2.7 cm) are exactly known. The third digit (0.03 cm) is uncertain because it was interpolated or estimated 1 digit beyond the smallest graduation.
7INTERPOLATION AND SIGNIFICANT FIGURES What is the volume of water in this graduated cylinder? Always measure the volume of a liquid at the bottom of the meniscus. The units are mL.The volume of water is 52.8 mL. The 52 mL are exactly known, and the 0.8 mL is uncertain because it was interpolated or estimated 1 digit beyond the smallest graduation.
8SIGNIFICANT FIGURES AND ZEROS Zeros between nonzero digits are significant. That is, 508 cm has 3 significant figures.Leading zeroes merely locate the decimal point and are never significant. That is, cm equals 4.97 x 10-2 cm and has 3 significant figures.Trailing zeros are significant as follows: 50.0 mL has 3 significant figures, 50. mL has 2 significant figures, and 50 mL has 1 significant figure.Datum (grams)Number of Significant FiguresDatum (milliliters)10,0341.9080.32150150.0.7050.0545.86 x 10-73040542332
9SIGNIFICANT FIGURES, ADDITION, AND SUBTRACTION When adding or subtracting do NOT extend the result beyond the first column with a doubtful figure. For example, …
10SIGNIFICANT FIGURES, ADDITION, AND SUBTRACTION What is ?What is ?
11SIGNIFICANT FIGURES, MULTIPLICATION, AND DIVISION When multiplying or dividing the answer will have the same number of significant digits as the least accurate number used to get the answer. For example, …2.005 g / 4.95 mL = g/mLWhat is x 2.6?What is / 2.6?
12SIGNIFICANT FIGURES AND CALCULATIONS THAT REQUIRE MULTIPLE STEPS An average is the best estimate of the true value of a parameter.A standard deviation is a measure of precision.Averages and standard deviations require several steps to calculate. You must keep track of the number of significant figures during each step. Do NOT discard or round any figures until the final number is reported.
13SIGNIFICANT FIGURES AND CALCULATIONS THAT REQUIRE MULTIPLE STEPS ∞Significant Figures2 Significant Figures1 Significant Figure1 Significant Figure1 Significant Figure0 Significant Figures
14What is average and standard deviation for the following 3 measurements of the same sample?
15SOURCESAmerican Public Health Association, American Water Works Association, Water Environment Federation Standard Methods for the Examination of Water and Wastewater. 19th ed. Washington, DC: American Public Health Association.Barnes, D.S., J.A. Chandler Chemistry Workbook and Laboratory Manual. Amherst, MA: University of Massachusetts.Christian, G.D Analytical Chemistry, 3rd ed. New York, NY: John Wiley & Sons, Inc.Frisbie, S.H., E.J. Mitchell, A.Z. Yusuf, M.Y. Siddiq, R.E. Sanchez, R. Ortega, D.M. Maynard, B. Sarkar The development and use of an innovative laboratory method for measuring arsenic in drinking water from western Bangladesh. Environmental Health Perspectives. 113(9):Morrison Laboratories Meniscus Madness. Available: [accessed 25 August 2006].