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Chapter 1: Problem 4

Say I own 857 CDs. My friend has written a computer program that uses a webcam to scan the shelves in my house where I keep my CDs and measure how many I have. His program says that I have 863 CDs. Define measurement error. What is the measurement error in my friend鈥檚 CD-counting device?

Short Answer

Expert verified
The measurement error in the CD-counting device is 6 CDs.

Step by step solution

01

Understanding Measurement Error

Measurement error is defined as the difference between the measured value and the true value. In this context, the measured value is what your friend's program counted, and the true value is the number of CDs you said you own.
02

Identifying True and Measured Values

The true value given in the problem is 857 CDs, and the measured value is 863 CDs. These two pieces of information are crucial to determine the measurement error.
03

Calculating Measurement Error

To find the measurement error, subtract the true value from the measured value: Measurement Error = Measured Value - True Value. Plug in the numbers: Measurement Error = 863 - 857 = 6.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Measured Value
The measured value is what a measuring tool or device, like your friend's program in the exercise, determines as the result of measurement. It is the output that the tool gives us after taking a measurement. In this example, the program measured the number of CDs as 863. This value is considered an 'estimate' of the true attribute being measured, which in this case, is the total number of CDs you own. Each time you use a measurement device, you obtain a measured value which can slightly vary due to various influences, like limitations or inaccuracies in the measuring device itself.
True Value
On the other hand, the true value is the accurate and exact quantity of the attribute being measured, without any errors or deviations. It represents what you aim to know or determine. In our example, the true value is the actual number of CDs you own, which is clearly stated as 857 CDs. The true value is more like a 'goal' or 'benchmark' when assessing an attribute, and it is not always readily available because of the presence of potential measurement errors or the difficulty in obtaining exact data. In scientific terms, achieving the true value with absolute certainty is quite rare, which makes it all the more important in measurements.
Calculation of Error
The calculation of error helps us understand by how much our measured value deviates from the true value. It is essential in evaluating the accuracy and reliability of our measurement tools or methods. To calculate the measurement error, you simply need to subtract the true value from the measured value:
  • Measurement Error = Measured Value - True Value
Knowing this formula is quite handy, as it allows you to compute the error for any measurement you take. In the exercise's context, inserting the values gives us:
  • Measurement Error = 863 - 857 = 6
This shows the error is 6 CDs, indicating the program overestimated the count.
Concept of Measurement Error
Measurement error is a crucial concept in any scientific or technical field where precision is necessary. It is the difference between the measured and true values of a quantity and is inevitable in any measurement to some degree. Understanding measurement error allows us to gauge the reliability of a measuring device or process.
  • Types of errors include systematic errors (consistent and predictable) and random errors (unpredictable and vary over measurements).
  • Knowing the measurement error helps us make necessary adjustments or calibrations to improve accuracy.
  • It provides insight into the limitations of a measurement system.
In real-world applications, acknowledging measurement errors allows users to maintain a level of skepticism and ensures that they use verification methods for higher confidence in results.

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Most popular questions from this chapter

Sports scientists sometimes talk of a 鈥榬ed zone鈥�, which is a period during which players in a team are more likely to pick up injuries because they are fatigued. When a player hits the red zone it is a good idea to rest them for a game or two. At a prominent London football club that I support, they measured how many consecutive games the 11 first team players could manage before hitting the red zone: 10, 16, 8, 9, 6, 8, 9, 11, 12, 19, 5. Calculate the mean, standard deviation, median, range and interquartile range.

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