🎯 Judging Accuracy and Precision

In science, judging the quality of your measurements is a critical skill. This guide will teach you how to check if your numbers are accurate (close to the true answer) and precise (close to each other).

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How to Judge Accuracy and Precision

Use these two calculations to decide if your measurements are good.

Step 1: Judge Accuracy with Percent Error

Percent error is a number that tells you exactly how close your measurements are to the true value. The smaller the percent error, the more accurate your measurements are.

To find it, you need a known true value to compare your measurements against.

\[\text{Percent Error} = \frac{|Experimental - True|}{True} \times 100\%\]

Note the absolute value signs are there so that your answer is always positive.

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Step 2: Judge Precision with Range

Precision tells you how consistent your measurements are with each other. The smaller the range, the more precise your measurements are.

The simplest way to calculate precision is to find the range, which is the difference between the highest and lowest measurements in your data set.

\[\text{Range} = \text{Highest Value} - \text{Lowest Value}\]

For Advanced Students: Use Standard Deviation

While the range is a quick way to check precision, standard deviation is a much more accurate measure. It considers every data point in your set, not just the two extremes, to give you a more reliable picture of the data's spread. A smaller standard deviation means higher precision. The formula is: $$ s = \sqrt{\frac{\sum_{i=1}^N (x_i - \bar{x})^2}{N-1}} $$

$s$: The standard deviation.

$x_i$: Each individual measurement in your data set.

$\bar{x}$: The average (mean) of all your measurements.

$N$: The total number of measurements.

Example: Using the data (9.85 g, 10.15 g, 9.95 g), the average is $9.98 \text{ g}$. The standard deviation is calculated as: $$ s = \sqrt{\frac{(9.85 - 9.98)^2 + (10.15 - 9.98)^2 + (9.95 - 9.98)^2}{3-1}} $$ $$ s = \sqrt{\frac{0.0169 + 0.0289 + 0.0009}{2}} \approx 0.15 \text{ g} $$

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Key Takeaways

• Accuracy vs. Precision: Accuracy is about being right, while precision is about being consistent.
• The Power of Numbers: Percent error gives you a precise number for accuracy, and the range gives you a number for precision. These numbers remove all guesswork.
• You Can’t Judge from One: You can’t assess precision from a single measurement. You need to measure something several times.

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Related Concepts & Skills

• Accuracy vs. Precision (Concept)

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Practice Problems

Test your understanding with these problems:

• No specific practice problems for judging accuracy and precision have been added yet.
• Accuracy and Precision Problems (Beginner)
• Accuracy and Precision Problems (Intermediate)
• Accuracy and Precision Problems (Challenging)