Types of Error
What type of error causes measurements to scatter randomly around the true value?
Random error
Accuracy describes how close a measurement is to what?
The true/accepted value.
What does measurement uncertainty tell us?
The range within which the true value is expected to lie / the limitation of our measurement.
A student reports a balance reading as 12.34567 g, but the balance only reads to 0.01 g. What is wrong?
Too many significant figures.
A graduated cylinder has markings every 1 mL. What is the estimated uncertainty of the measurement?
±0.5 mL
A balance consistently reads 0.003 g too high. What type of error is this?
Systematic error
Precision describes what?
How closely repeated measurements agree with one another.
A measurement is 25.0 ± 0.2 mL. What does ±0.2 mL represent?
The uncertainty of the measurement.
Why do analytical chemists make multiple measurements of the same sample?
To evaluate variability/reproducibility and detect unusual results.
A measurement is 25.0 ± 0.2 mL. What is the absolute uncertainty?
±0.2 mL
A student gets 10.21, 10.20, 10.22, and 10.21 g when the true value is 10.50 g. What can you say about the measurements?
High precision, low accuracy.
A student measures a sample three times and gets:
9.98 g, 10.01 g, 10.00 g
The accepted value is 10.00 g.
Is the data accurate, precise, both, or neither?
Both accurate and precise.
A balance reads 2.50 ± 0.01 g. What is the relative uncertainty?
2.500.01=0.004
or 0.4%
A dataset is 24.1, 24.2, 24.0, 24.1, 31.7 mg/L. What should the analyst investigate?
The 31.7 mg/L result as a possible outlier.
A measurement is 50.0 ± 0.5 g. What is the relative uncertainty?
1%
Your calibration curve consistently produces concentrations that are 5% too high. What type of error might be responsible?
Systematic error
Which dataset is more precise? Which is more accurate?
If A=10.0±0.2 and B=5.0±0.1, what is the uncertainty in A+B?
For addition/subtraction:
uA+B= (uA2+uB2)^(1/2)
A calibration curve has an R² value of 0.998. What does this tell you about the linear relationship?
There is a very strong linear relationship.
A measurement is 20.0 ± 0.4 mL. What is the percent uncertainty?
2%
A balance has a +0.03 g calibration error. A student measures a 10.00 g sample five times:
10.21, 10.17, 10.24, 10.19, 10.22 g
What types of error are present?
A method has a low % error but a high %RSD. Is it accurate, precise, both, or neither?
Accurate but not precise.
Calculate the relative uncertainty of:
A=2.0±0.1(10.0±0.2)(5.0±0.1)
6.2%
A student gets an unexpected result. Which would be most useful for determining whether the result is reliable: repeat the measurement, change the answer, or ignore the result?
Repeat the measurement.
If A=10.0±0.2 and B=5.0±0.1, what is the uncertainty in A+B?
±0.22 (approximately)