1.5 Measurement Uncertainty, Accuracy, and Precision
3 min read•june 24, 2024
Measurement and are crucial in chemistry. measures closeness to true values, while reflects consistency in repeated measurements. Understanding these concepts helps interpret data reliability and experimental results.
, rules, and error analysis are essential tools for managing . These techniques ensure meaningful data interpretation, allowing chemists to communicate results effectively and make informed decisions based on experimental outcomes.
Measurement and Uncertainty
Accuracy vs precision in measurements
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Introduction to Statistical vs. Systematic Uncertainty – Physics 132 Lab Manual View original
measures how close a result is to the true or accepted value
High accuracy indicates the measured value is very close to the true value ( on a )
Low accuracy means the measured value differs significantly from the true value (off-center hits on a dartboard)
describes how close multiple measurements are to each other, regardless of their accuracy
High precision means the measurements are tightly clustered, even if they are not centered around the true value (tightly grouped darts, but not necessarily in the bullseye)
Low precision indicates the measurements are widely dispersed, even if their average is close to the true value (scattered darts across the board)
Measurements can be categorized as:
Accurate and precise: close to the true value and tightly clustered (bullseye with tightly grouped darts)
Accurate but imprecise: close to the true value but widely dispersed (darts centered around the bullseye but scattered)
Precise but inaccurate: tightly clustered but far from the true value (tightly grouped darts off-center)
Neither accurate nor precise: far from the true value and widely dispersed (scattered darts off-center)
Exact vs uncertain chemical data
have no uncertainty and are not subject to significant figure rules
Counted values (5 molecules)
Defined values (1 kg = 1000 g)
Integers in chemical formulas (H2SO4)
have inherent uncertainty and follow significant figure rules
Measured values (5.3 g, 10.2 mL)
Calculated values derived from measured values (density = mass ÷ volume)
Significant figures for uncertainty
represent the number of certain digits plus one uncertain digit in a measurement
Non-zero digits are always significant (1, 2, 3, ..., 9)
Zeros between non-zero digits are significant (1.0023)
Leading zeros are not significant (0.0012 has two significant figures)
Trailing zeros are significant only with a decimal point (1.200 has four significant figures, 1200 has two)
When multiplying or dividing, the result should have the same number of significant figures as the measurement with the fewest significant figures
5.2×3.10=16.12, rounded to 16 (two significant figures)
When adding or subtracting, the result should have the same number of decimal places as the measurement with the fewest decimal places
5.2+3.10=8.30, rounded to 8.3 (one decimal place)
Rounding rules in calculations
If the digit to the right of the last significant figure is less than 5, round down (12.44 rounds to 12.4)
If the digit to the right of the last significant figure is 5 or greater, round up (12.45 rounds to 12.5)
If the digit to the right of the last significant figure is 5 followed by zeros:
Round up if the last significant figure is odd (12.350 rounds to 12.4)
Round down if the last significant figure is even (12.450 rounds to 12.4)
Sources of Error and Statistical Analysis
: consistent deviation from the true value due to flaws in equipment or methodology (e.g., uncalibrated instruments)
: unpredictable fluctuations in measurements due to limitations in precision (e.g., human reaction time)
: a measure of the spread of data points around the mean, indicating precision
: a range of values that likely contains the true value, based on the standard deviation
: the process of adjusting instruments to reduce systematic errors and improve accuracy
: the way uncertainties in individual measurements combine to affect the uncertainty of a final calculated result