Difference between Accuracy and precision

1. • Accuracy is the closeness of a measured value to the trueAccuracy is the closeness of a measured value to the true
value.value.
• For example, the measured density of water has become moreFor example, the measured density of water has become more
accurate with improved experimental design, technique, andaccurate with improved experimental design, technique, and
equipment.equipment.
ACCURACYACCURACY
Density of HDensity of H22O at 20° CO at 20° C
(g/cm(g/cm33
))
11
1.01.0
1.001.00
0.9980.998
0.99820.9982
0.998200.99820
0.9982030.998203

2. • Percent error is used to estimate the accuracy of aPercent error is used to estimate the accuracy of a
measurement.measurement.
• Percent error will always be a positive.Percent error will always be a positive.
• What is the percent error if the measured density of titanium (Ti)What is the percent error if the measured density of titanium (Ti)
is 4.45 g/cmis 4.45 g/cm33
and the accepted density of Ti is 4.50 g/cmand the accepted density of Ti is 4.50 g/cm33
??
ACCURACYACCURACY

3. Average = 15.3 μg/LAverage = 15.3 μg/L
Standard Deviation = 2.1 μg/LStandard Deviation = 2.1 μg/L
What is the true concentration of As in this experiment?What is the true concentration of As in this experiment?
Estimate the accuracy of this method.Estimate the accuracy of this method.
How precise is this method?How precise is this method?
• Precision is the agreement between repeated measurements of thePrecision is the agreement between repeated measurements of the
same sample. Precision is usually expressed as a standard deviation.same sample. Precision is usually expressed as a standard deviation.
• For example, the precision of a method for measuring arsenic (As) wasFor example, the precision of a method for measuring arsenic (As) was
determined by measuring 7 different solutions each containing 14.3 μg/L ofdetermined by measuring 7 different solutions each containing 14.3 μg/L of
As.As.
PRECISIONPRECISION
MeasuredMeasured
ConcentrationConcentration
(μg/L)(μg/L)
18.418.4
13.613.6
13.613.6
14.214.2
16.016.0
13.613.6
17.817.8
14.3 μg/L14.3 μg/L
2.1 μg/L2.1 μg/L

4. • Describe the accuracy and precision of these 4 targets.Describe the accuracy and precision of these 4 targets.
ACCURACY AND PRECISIONACCURACY AND PRECISION
Accurate, andAccurate, and
preciseprecise
Precise, butPrecise, but
not accuratenot accurate
Accurate, butAccurate, but
not precisenot precise
Not accurate,Not accurate,
and notand not
preciseprecise

5. • Systematic (or determinate) errors are reproducible andSystematic (or determinate) errors are reproducible and
cause a bias in the same direction for each measurement.cause a bias in the same direction for each measurement.
• For example, a poorly trained operator that consistently makesFor example, a poorly trained operator that consistently makes
the same mistake will cause systematic error. Systematic errorthe same mistake will cause systematic error. Systematic error
can be corrected.can be corrected.
• Random (or indeterminate) errors are caused by the naturalRandom (or indeterminate) errors are caused by the natural
uncertainty that occurs with any measurement.uncertainty that occurs with any measurement.
• Random errors obey the laws of probability. That is, randomRandom errors obey the laws of probability. That is, random
error might cause a value to be over predicted during its firsterror might cause a value to be over predicted during its first
measurement and under predicted during its secondmeasurement and under predicted during its second
measurement. Random error cannot be corrected.measurement. Random error cannot be corrected.
ERRORSERRORS

6. • By convention, a measurement is recorded by writing all exactlyBy convention, a measurement is recorded by writing all exactly
known numbers and 1 number which is uncertain, together withknown numbers and 1 number which is uncertain, together with
a unit label.a unit label.
• All numbers written in this way, including the uncertain digit, areAll numbers written in this way, including the uncertain digit, are
called significant figures.called significant figures.
• For example, the blue line is 2.73 cm long. This measurementFor example, the blue line is 2.73 cm long. This measurement
has 3 significant figures. The first 2 digits (2.7 cm) are exactlyhas 3 significant figures. The first 2 digits (2.7 cm) are exactly
known. The third digit (0.03 cm) is uncertain because it wasknown. The third digit (0.03 cm) is uncertain because it was
interpolated or estimated 1 digit beyond the smallestinterpolated or estimated 1 digit beyond the smallest
graduation.graduation.
INTERPOLATION AND SIGNIFICANT FIGURESINTERPOLATION AND SIGNIFICANT FIGURES

7. • What is the volume of water in this graduated cylinder? AlwaysWhat is the volume of water in this graduated cylinder? Always
measure the volume of a liquid at the bottom of the meniscus.measure the volume of a liquid at the bottom of the meniscus.
The units are mL.The units are mL.
• The volume of water is 52.8 mL. The 52 mL are exactly known,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 orand the 0.8 mL is uncertain because it was interpolated or
estimated 1 digit beyond the smallest graduation.estimated 1 digit beyond the smallest graduation.
INTERPOLATION AND SIGNIFICANT FIGURESINTERPOLATION AND SIGNIFICANT FIGURES

8. • Zeros between nonzero digits are significant. That is, 508 cmZeros between nonzero digits are significant. That is, 508 cm
has 3 significant figures.has 3 significant figures.
• Leading zeroes merely locate the decimal point and are neverLeading zeroes merely locate the decimal point and are never
significant. That is, 0.0497 cm equals 4.97 x 10significant. That is, 0.0497 cm equals 4.97 x 10-2-2
cm and has 3cm and has 3
significant figures.significant figures.
• Trailing zeros are significant as follows: 50.0 mL has 3Trailing zeros are significant as follows: 50.0 mL has 3
significant figures, 50. mL has 2 significant figures, and 50 mLsignificant figures, 50. mL has 2 significant figures, and 50 mL
has 1 significant figure.has 1 significant figure.
SIGNIFICANT FIGURES AND ZEROSSIGNIFICANT FIGURES AND ZEROS
DatumDatum
(grams)(grams)
Number ofNumber of
SignificantSignificant
FiguresFigures
DatumDatum
(milliliters)(milliliters)
Number ofNumber of
SignificantSignificant
FiguresFigures
10,03410,034
1.9081.908
0.320.32
0.000460.00046
150150
0.00001600.0000160
150.150.
0.7050.705
0.0540.054
5.86 x 105.86 x 10-7-7
30403040
0.00007300.0000730
55
44
22
22
22
33
33
33
22
33
33
33

9. • When adding or subtracting do NOT extend the result beyondWhen adding or subtracting do NOT extend the result beyond
the first column with a doubtful figure. For example, …the first column with a doubtful figure. For example, …
SIGNIFICANT FIGURES, ADDITION, AND SUBTRACTIONSIGNIFICANT FIGURES, ADDITION, AND SUBTRACTION

10. • What is 16.874 + 2.6?What is 16.874 + 2.6?
• What is 16.874 - 2.6?What is 16.874 - 2.6?
SIGNIFICANT FIGURES, ADDITION, AND SUBTRACTIONSIGNIFICANT FIGURES, ADDITION, AND SUBTRACTION

11. • When multiplying or dividing the answer will have the sameWhen multiplying or dividing the answer will have the same
number of significant digits as the least accurate number usednumber of significant digits as the least accurate number used
to get the answer. For example, …to get the answer. For example, …
2.005 g / 4.95 mL = 0.405 g/mL2.005 g / 4.95 mL = 0.405 g/mL
• What is 16.874 x 2.6?What is 16.874 x 2.6?
• What is 16.874 / 2.6?What is 16.874 / 2.6?
SIGNIFICANT FIGURES, MULTIPLICATION, AND DIVISIONSIGNIFICANT FIGURES, MULTIPLICATION, AND DIVISION

12. • AnAn averageaverage is the best estimate of the true value of ais the best estimate of the true value of a
parameter.parameter.
• AA standard deviationstandard deviation is a measure of precision.is a measure of precision.
• Averages and standard deviations require several steps toAverages and standard deviations require several steps to
calculate. You must keep track of the number of significantcalculate. You must keep track of the number of significant
figures during each step. Dofigures during each step. Do NOTNOT discard or round any figuresdiscard or round any figures
until the final number is reported.until the final number is reported.
SIGNIFICANT FIGURES AND CALCULATIONS THATSIGNIFICANT FIGURES AND CALCULATIONS THAT
REQUIRE MULTIPLE STEPSREQUIRE MULTIPLE STEPS

13. SIGNIFICANT FIGURES AND CALCULATIONS THATSIGNIFICANT FIGURES AND CALCULATIONS THAT
REQUIRE MULTIPLE STEPSREQUIRE MULTIPLE STEPS
2 Significant
Figures
1 Significant Figure
2 Significant Figures
0 Significant Figures
1 Significant Figure
1 Significant Figure
Significant Figures∞

14. • What is average and standard deviation for the following 3What is average and standard deviation for the following 3
measurements of the same sample?measurements of the same sample?

15. • American Public Health Association, American Water Works Association,American Public Health Association, American Water Works Association,
Water Environment Federation. 1995. Standard Methods for the ExaminationWater Environment Federation. 1995. Standard Methods for the Examination
of Water and Wastewater. 19th ed. Washington, DC: American Public Healthof Water and Wastewater. 19th ed. Washington, DC: American Public Health
Association.Association.
• Barnes, D.S., J.A. Chandler. 1982. Chemistry 111-112 Workbook andBarnes, D.S., J.A. Chandler. 1982. Chemistry 111-112 Workbook and
Laboratory Manual. Amherst, MA: University of Massachusetts.Laboratory Manual. Amherst, MA: University of Massachusetts.
• Christian, G.D. 1986. Analytical Chemistry, 3rd ed. New York, NY: JohnChristian, G.D. 1986. Analytical Chemistry, 3rd ed. New York, NY: John
Wiley & Sons, Inc.Wiley & Sons, Inc.
• Frisbie, S.H., E.J. Mitchell, A.Z. Yusuf, M.Y. Siddiq, R.E. Sanchez, R.Frisbie, S.H., E.J. Mitchell, A.Z. Yusuf, M.Y. Siddiq, R.E. Sanchez, R.
Ortega, D.M. Maynard, B. Sarkar. 2005. The development and use of anOrtega, D.M. Maynard, B. Sarkar. 2005. The development and use of an
innovative laboratory method for measuring arsenic in drinking water frominnovative laboratory method for measuring arsenic in drinking water from
western Bangladesh. Environmental Health Perspectives. 113(9):1196-1204.western Bangladesh. Environmental Health Perspectives. 113(9):1196-1204.
• Morrison Laboratories. 2006. Meniscus Madness. Available:Morrison Laboratories. 2006. Meniscus Madness. Available:
http://www.morrisonlabs.com/meniscus.htmhttp://www.morrisonlabs.com/meniscus.htm [accessed 25 August 2006].[accessed 25 August 2006].
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