Question

Which of the following are systematic errors? a. A colorblind person who repeatedly runs red lights. b. An accountant whose occasional math errors are sometimes on the high side and sometimes on the low side. c. The tendency many people have to see faces in clouds. d. Miranda paying good money for a nice-looking apple that turns out to be rotten inside. e. Elvis always wanting to save more but then spending his whole paycheck, month after month.

Short answer

Options a and e are systematic errors.

Step-by-step solution

Define Systematic Errors

Systematic errors are consistent, repeatable errors associated with faulty equipment or a flawed experiment design, which cause a bias in measurement.

Analyze Each Option

Let's look at each option individually to determine if it represents a systematic error: - a) A colorblind person who consistently runs red lights shows a repetitive pattern due to a consistent perception issue, indicating a systematic error. - b) An accountant whose mistakes are sometimes high and sometimes low indicates random errors, not systematic. - c) The tendency to see faces in clouds is a perceptual illusion which does not represent a systematic measurement error. - d) Buying an apple that looks good but is rotten inside is a one-time misleading outcome, not a systematic error. - e) Consistently failing to save money despite an intention to save shows a repetitive pattern due to a consistent behavior, indicating a systematic error.

Key concepts

Systematic Error Definition

Systematic errors are a type of measurement error that occurs consistently across repeated measurements or observations. This means that every time the measurement is made, the same mistake occurs in the same way. These errors are not due to random chance or variability but rather are a result of a flaw in equipment, methodology, or observer condition. Because systematic errors are consistent, they can cause a bias, typically leading to measurements that are consistently too high or too low compared to the actual value.

For example, if a scale consistently reads 1 kg heavier than an object's actual weight, this is a systematic error. Systematic errors can drastically affect results and conclusions derived from an experiment, which is why they are often prioritized for adjustment or correction when analyzing data.

Examples of Systematic Errors

Understanding examples can help in identifying systematic errors in real-life scenarios. Let's look into some common examples:

• A broken thermometer that always reads 2°C higher than the actual temperature. This would systematically overestimate temperature readings.
• In the given exercise, a colorblind person's consistent tendency to miss red traffic lights when driving is a systematic error due to a continuous perception issue.
• An incorrectly calibrated scale that skews all measurements up by 5 grams creates a systematic error whenever it is used.
• Similarly, repeatedly misjudging the quality of an apple based on its appearance, as in the exercise scenario, would be another example if the decision-making process is flawed.

These examples demonstrate how systematic errors can arise due to equipment failures, physiological limitations, or biases in perception and evaluation.

Systematic vs Random Errors

Systematic and random errors are two main types of errors that can occur in measurements and experiments. It is crucial to differentiate between them in order to effectively address their impacts.

Systematic errors are consistent and repeatable, leading to predictable and reproducible deviations from the true value. They typically arise from persistent issues such as improperly calibrated equipment or a flawed method that biases the results in one direction.

In contrast, random errors are typically unpredictable and vary in magnitude and direction each time a measurement is made. These errors result from unknown or unpredictable changes during the measurement process, like sudden environmental shifts or human reaction time variability. For example, in the given exercise, an accountant whose errors sometimes lead to overestimates and other times to underestimates would be experiencing random errors.

Dealing with these errors requires different strategies: systematic errors usually need adjustments to methodologies or equipment, while random errors can be minimized by increasing the number of observations or trials.