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Chapter 1: Problem 22

What is the difference between random error and systematic error?

Short Answer

Expert verified
The key difference between random error and systematic error is that random error is unpredictable and fluctuates erratically, averaging out as the number of measurements increases, whereas systematic error is consistent and persistent over multiple measurements, leading to a deviation from the true value that doesn't average out. Random errors can be minimized by increasing the number of measurements and employing statistical analysis, while systematic errors can be prevented by proper calibration, experimental setup, and unbiased observation.

Step by step solution

01

Define Random Error

Random error, also known as statistical error, refers to the unpredictable and erratic fluctuations in measurements that occur due to various factors like noise in the measuring equipment, environmental conditions, or the observer's slight errors. These errors can occur in both directions, either being higher or lower than the true value, and tend to average out as the number of measurements increases.
02

Define Systematic Error

Systematic error, also known as a bias, is a consistent and repeatable error that occurs during measurements. These errors are caused by factors like an improperly calibrated instrument, observer bias, or incorrect experimental setup. Systematic errors result in a consistent deviation from the true value and do not average out over multiple measurements.
03

Example of Random Error

Let's say you have a digital scale and want to measure the weight of an object. Depending on factors such as vibrations, fluctuations in power supply, or reading the display at a slight angle (parallax error), the weight might read slightly different values each time you measure the object. These fluctuations in readings are random errors.
04

Example of Systematic Error

Now, let's assume the same digital scale reads consistently 5 grams higher than the true weight of any object placed on it. This means the scale is improperly calibrated, leading to a systematic error of +5 grams in each measurement. No matter how many times you measure an object's weight, the scale will always read 5 grams more than it actually weighs.
05

Key Differences

In summary, random error is unpredictable and fluctuates erratically, averaging out as the number of measurements increases. Systematic error is consistent and persistent over multiple measurements, leading to a deviation from the true value that doesn't average out. To minimize random errors, one can increase the number of measurements and employ statistical analysis. To prevent systematic errors, proper calibration, experimental setup, and unbiased observation are needed.

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Most popular questions from this chapter

Precious metals and gems are measured in troy weights in the English system: $$\begin{aligned} 24 \text { grains } &=1 \text { pennyweight (exact) } \\ 20 \text { pennyweight } &=1 \text { troy ounce (exact) } \\ 12 \text { troy ounces } &=1 \text { troy pound (exact) } \\ 1 \operatorname{grain} &=0.0648 \mathrm{g} \\ 1 \text { carat } &=0.200 \mathrm{g} \end{aligned}$$ a. The most common English unit of mass is the pound avoirdupois. What is 1 troy pound in kilograms and in pounds? b. What is the mass of a troy ounce of gold in grams and in carats? c. The density of gold is 19.3 \(\mathrm{g} / \mathrm{cm}^{3} .\) What is the volume of a troy pound of gold?

The density of osmium is reported by one source to be \(22,610 \mathrm{kg} / \mathrm{m}^{3} .\) What is this density in \(\mathrm{g} / \mathrm{cm}^{3} ?\) What is the mass of a block of osmium measuring 10.0 \(\mathrm{cm} \times 8.0 \mathrm{cm} \times 9.0 \mathrm{cm} ?\)

Diamonds are measured in carats, and 1 carat \(=0.200 \mathrm{g} .\) The density of diamond is 3.51 \(\mathrm{g} / \mathrm{cm}^{3}\) . a. What is the volume of a 5.0 -carat diamond? b. What is the mass in carats of a diamond measuring 2.8 \(\mathrm{mL} ?\)

During a very cold winter, the temperature may remain below freezing for extended periods. However, fallen snow can still disappear, even though it cannot melt. This is possible because a solid can vaporize directly, without passing through the liquid state. Is this process (sublimation) a physical or a chemical change?

a. There are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour. Use these data to determine how many minutes are in a month. b. Now use the following data to calculate the number of minutes in a month: 24 hours per day, 60 minutes per hour, 7 days per week, and 4 weeks per month. c. Why are these answers different? Which (if any) is more correct? Why?
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