The following dartboards illustrate the types of errors...

Name: Problem 73, Chapter 1: Chemistry: The Molecular Nature of Matter and Change
Uploaded: 2023-08-19T18:16:10-08:00
Channel: Susan Hallstrom
Description: The following dartboards illustrate the types of errors often seen in measurements. The bull’s-eye represents the actual value, and the darts represent the data. (a) Which experiments yield the same average result? (b) Which experiment(s) display(s) high precision? (c) Which experiment(s) display(s) high accuracy? (d) Which experiment(s) show(s) a systematic error?

The following dartboards illustrate the types of errors often seen in measurements. The bull’s-eye represents the actual value, and the darts represent the data. (a) Which experiments yield the same average result? (b) Which experiment(s) display(s) high precision? (c) Which experiment(s) display(s) high accuracy? (d) Which experiment(s) show(s) a systematic error?

The following dartboards illustrate the types of errors often seen in measurements. The bull’s-eye represents the actual value, and the darts represent the data.
(a) Which experiments yield the same average result?
(b) Which experiment(s) display(s) high precision?
(c) Which experiment(s) display(s) high accuracy?
(d) Which experiment(s) show(s) a systematic error?

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Key Concepts

Arithmetic Mean

The arithmetic mean, or average, is a statistical measure calculated by summing all data points and dividing by their count. It is used as a central value to compare different sets of measurements, especially when evaluating consistent results across multiple experiments.

Systematic Error

Systematic error is a consistent bias in measurements that causes them to deviate in a uniform direction from the true value. Such errors arise due to flaws in the measurement system or procedure and affect accuracy by shifting the mean value.

Random Error

Random error consists of unpredictable fluctuations in measurement which may cause variability in data points. These errors affect the precision of an experiment since they introduce scatter in the repeated measurements.

Accuracy

Accuracy refers to how close the measurements are to the true or accepted value. It indicates the correctness of an experiment, meaning that high accuracy implies that the average measurement is near the actual value, even if the measurements themselves are not consistent.

Precision

Precision describes the degree to which repeated measurements under the same conditions yield the same result. It is concerned with the variability among measurements rather than their closeness to the true value, so high precision means the data points are clustered together.

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