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Questions and Answers
The mean is the most widely used measure of central value in statistics.
The mean is the most widely used measure of central value in statistics.
True (A)
The median is the result in the exact middle of replicate data when arranged in order.
The median is the result in the exact middle of replicate data when arranged in order.
True (A)
Analyzing replicates allows us to estimate the precision of the individual measurements.
Analyzing replicates allows us to estimate the precision of the individual measurements.
True (A)
The central value of a set is usually higher than any of the individual results.
The central value of a set is usually higher than any of the individual results.
When calculating the median for an even number of results, the average of the middle pair is used.
When calculating the median for an even number of results, the average of the middle pair is used.
Replicates are not necessary when trying to improve the reliability of analytical procedures.
Replicates are not necessary when trying to improve the reliability of analytical procedures.
Precision describes the agreement among several results obtained in the same way.
Precision describes the agreement among several results obtained in the same way.
Accuracy measures how scattered data is around the mean value.
Accuracy measures how scattered data is around the mean value.
Systematic errors may cause the mean of a data set to differ from the accepted value.
Systematic errors may cause the mean of a data set to differ from the accepted value.
Random errors are also known as determinate errors.
Random errors are also known as determinate errors.
Personal errors in measurements often require personal judgments.
Personal errors in measurements often require personal judgments.
Systematic method errors are usually related to the incorrect use of measuring devices.
Systematic method errors are usually related to the incorrect use of measuring devices.
Proportional errors are caused by random fluctuations in the measurement process.
Proportional errors are caused by random fluctuations in the measurement process.
Constant errors have a fixed magnitude regardless of the quantity being measured.
Constant errors have a fixed magnitude regardless of the quantity being measured.
Indeterminate errors cause data to be scattered around a mean value.
Indeterminate errors cause data to be scattered around a mean value.
Precision is expressed in terms of either absolute or relative error.
Precision is expressed in terms of either absolute or relative error.
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Study Notes
Improving Reliability
- To improve the reliability of results, 2-5 portions (replicates) of a sample are carried through an entire analytical procedure.
- The central value of a set of measurements is considered the "best" estimate, often represented by the mean or median.
The Mean and the Median
- The mean (arithmetic mean or average) is the most widely used measure of central value, calculated by dividing the sum of replicate measurements by the number of measurements.
- The median is the middle result when replicate data are arranged in increasing or decreasing order.
- For an odd number of results, the median is the middle result; for an even number, the average value of the middle pair is used.
Precision and Accuracy
- Precision describes the reproducibility of measurements, or the closeness of results obtained in exactly the same way.
- Accuracy indicates the closeness of the measurement to the true or accepted value, expressed by the error.
- Precision can be determined by measuring replicate samples, while accuracy is often more difficult to determine due to unknown true values.
Types of Errors
- Random (indeterminate) error causes data to scatter symmetrically around a mean value.
- Systematic (determinate) error causes the mean of a data set to differ from the accepted value.
- Gross error is a rare, large error that can cause a result to be either high or low.
Systematic Errors
- Instrumental errors occur due to measuring devices, such as pipets, burets, and volumetric flasks, holding or delivering volumes slightly different from those indicated.
- Method errors occur due to non-ideal chemical or physical behavior of reagents and reactions.
- Personal errors occur due to personal judgments, such as estimating the position of a pointer between two scale divisions.
Effect of Systematic Errors
- Constant errors become more serious as the size of the quantity measured decreases.
- Proportional errors occur due to the presence of interfering contaminants in the sample, causing high results for the percentage of copper.
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