Introduction to Taking Readings
In Physics, doing an experiment isn't just about getting an answer; it’s about getting a reliable answer. When you sit for your Unit 3 exam, you will often be asked to look at data collected by a student and decide if it is "good" or "bad." In this chapter, we will learn how to choose the right range of values, why repeats are your best friend in the lab, and how to spot a "weird" result known as an anomaly.
Practical skills are the foundation of everything we know in science. Even if you find the math in Unit 1 and Unit 2 challenging, mastering these practical concepts can help you pick up significant marks in Unit 3.
1. Range and Number of Readings
When you perform an experiment, the independent variable is the thing you change. The range is the difference between the highest and lowest values you choose for this variable.
Choosing the Right Range
To see a clear pattern in your data, your range should be as wide as possible within the limits of your equipment. For example, if you are investigating how the current in a bulb changes with potential difference (Unit 2), using a range of \(0.5\text{ V}\) to \(1.0\text{ V}\) is too small to see a curve. A range of \(0.0\text{ V}\) to \(6.0\text{ V}\) is much better!
How Many Readings?
In the Pearson Edexcel International AS Level, a good rule of thumb is to take at least six different sets of readings across your range. This ensures that when you plot a graph later, you have enough points to see if the relationship is a straight line or a curve.
Quick Tip: Ensure your readings are spread out evenly. If you are measuring the length of a wire from \(10\text{ cm}\) to \(60\text{ cm}\), take readings at \(10\text{, } 20\text{, } 30\text{, } 40\text{, } 50\text{, and } 60\text{ cm}\).
Key Takeaway: A wide range with at least six evenly spaced readings gives the most reliable picture of how one thing affects another.
2. Repeat Readings
Even the best physicists make small, random errors. Maybe you reacted a bit slowly with a stopwatch, or maybe you read a scale from a slightly different angle. This is why we repeat readings.
Precision and Repeatability
The syllabus defines these terms very specifically:
• Precision: How close your repeated measurements are to each other.
• Repeatability: The precision obtained when one person uses the same method and same equipment over a short period of time.
Calculating Uncertainty from Repeats
When you have a set of repeat readings, you should calculate a mean (average). However, repeats also allow us to calculate the uncertainty. In this course, the uncertainty of a set of repeats is calculated as half the range.
\(\text{Uncertainty} = \frac{\text{Maximum reading} - \text{Minimum reading}}{2}\)
Example: You measure the diameter of a wire three times: \(0.24\text{ mm}\), \(0.26\text{ mm}\), and \(0.25\text{ mm}\).
The range is \(0.26 - 0.24 = 0.02\text{ mm}\).
The uncertainty is \(\frac{0.02}{2} = 0.01\text{ mm}\).
Did you know? A measurement is usually considered repeatable if the percentage uncertainty is below 5%. If it's higher than that, you might need to rethink your technique!
Key Takeaway: Repeating readings helps reduce the effect of random errors and allows you to calculate the uncertainty in your data.
3. Identifying and Handling Anomalies
An anomaly is a reading that does not fit the pattern of the others. It is an "outlier."
How to spot them
1. In a table: Look at your repeats. If you have \(10.1\text{ s}\), \(10.2\text{ s}\), and \(14.5\text{ s}\), that \(14.5\text{ s}\) is clearly an anomaly.
2. On a graph: When you plot your points, an anomaly will be a point that sits far away from your line of best fit.
What to do with an anomaly?
In the Unit 3 exam, you might be asked to "criticise" a student's data. If you see an anomaly, you should:
• Identify it: State clearly which reading is inconsistent.
• Check it: If you are still in the lab, re-take that specific measurement.
• Exclude it: When calculating the mean, do not include the anomalous result. Cross it out and average the remaining "good" readings.
Common Mistake: Don't just ignore an anomaly without mentioning it! In an exam, you must show that you recognized it wasn't part of the pattern.
Key Takeaway: Anomalies are inconsistent results. Identify them, exclude them from your mean, and ideally repeat the measurement to get a better value.
4. Accuracy vs. Precision
These two words are often used interchangeably in everyday life, but in Physics, they mean very different things.
• Accuracy: How close your measurement is to the true value. (Think of hitting the bullseye on a dartboard).
• Precision: How close your measurements are to each other. (Think of hitting the same spot on the dartboard over and over, even if it's not the bullseye).
If your results are precise (close together) but not accurate (far from the true value), you might have a systematic error, such as a "zero error" on your instrument. (To learn more about instruments and zero errors, see the chapter on "Instruments, resolution and measuring technique.")
Quick Review: The Checklist for Great Readings
To succeed in Unit 3 questions about taking readings, keep this checklist in mind:
1. Is the range wide enough? (e.g., using the full capacity of the ruler or voltmeter).
2. Are there enough readings? (At least six sets).
3. Are there repeats? (At least three readings for each value to calculate a mean).
4. Are there anomalies? (Check if any repeats are "way off" and exclude them from the mean).
5. Is the uncertainty calculated correctly? (Use half the range of your repeats: \( \frac{\text{max} - \text{min}}{2} \)).
Encouraging Note: If calculating uncertainties feels difficult at first, just remember the "half the range" rule. It is the most common way to handle repeat data in your IAS exams!