Start studying BIOL 2604: Measuring Microbial Growth. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Propagation of Errors in Dilution Problems When a calculation is done in lab, it is important to round the result to the number of significant figures indicated by the precision of.

All science experiments contain error, so it’s important to know the types of error and how to calculate it. (Image: NASA/GSFC/Chris Gunn) Science labs usually ask you to compare your results against theoretical or known values. This helps you evaluate your results and compare them against other people’s values. The difference between your results and the expected or theoretical results is called error. The amount of error that is acceptable depends on the experiment, but a margin of error of 10% is generally considered acceptable. If there is a large margin of error, you’ll be asked to go over your procedure and identify any mistakes you may have made or places where error might have been introduced.

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So, you need to know the different types and sources of error and how to calculate them. How to Calculate Absolute Error One method of measuring error is by calculating absolute error, which is also called absolute uncertainty. This measure of accuracy is reported using the units of measurement. Absolute error is simply the difference between the measured value and either the true value or the average value of the data.

Absolute error = measured value – true value For example, if you measure gravity to be 9.6 m/s 2 and the true value is 9.8 m/s 2, then the absolute error of the measurement is 0.2 m/s 2. You could report the error with a sign, so the absolute error in this example could be -0.2 m/s 2. If you measure the length of a sample three times and get 1.1 cm, 1.5 cm, and 1.3 cm, then the absolute error is +/- 0.2 cm or you would say the length of the sample is 1.3 cm (the average) +/- 0.2 cm. Some people consider absolute error to be a measure of how accurate your measuring instrument is. If you are using a ruler that reports length to the nearest millimeter, you might say the absolute error of any measurement taken with that ruler is to the nearest 1 mm or (if you feel confident you can see between one mark and the next) to the nearest 0.5 mm. How to Calculate Relative Error Relative error is based on the absolute error value.

It compares how large the error is to the magnitude of the measurement. So, an error of 0.1 kg might be insignificant when weighing a person, but pretty terrible when weighing a apple. Relative error is a fraction, decimal value, or percent.

Relative Error = Absolute Error / Total Value For example, if your speedometer says you are going 55 mph, when you’re really going 58 mph, the absolute error is 3 mph / 58 mph or 0.05, which you could multiple by 100% to give 5%. Relative error may be reported with a sign.

In this case, the speedometer is off by -5% because the recorded value is lower than the true value. Because the absolute error definition is ambiguous, most lab reports ask for percent error or percent difference. How to Calculate Percent Error The most common error calculation, which is used when comparing your results against a known, theoretical, or accepted value.

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As you probably guess from the name, percent error is expressed as a percentage. It is the absolute (no negative sign) difference between your value and the accepted value, divided by the accepted value, multiplied by 100% to give the percent. % error = [accepted – experimental ] / accepted x 100% How to Calculate Percent Difference Another common error calculation is called percent difference. It is used when you are comparing one experimental result to another. In this case, no result is necessarily better than another, so the percent difference is the absolute value (no negative sign) of the difference between the values, divided by the average of the two numbers, multiplied by 100% to give a percentage:% difference = [experimental value – other value] / average x 100% Sources and Types of Error Every experimental measurement, no matter how carefully you take it, contains some amount of uncertainty or error. You are measuring against a standard, using an instrument that can never perfectly duplicate the standard, plus you’re human, so you might introduce errors based on your technique. The three main categories of errors are systematic errors, random errors, and personal errors.

Here’s what these types of errors are and common examples. Systematic Errors Systematic error affects all the measurements you take. All of these errors will be in the same direction (greater than or less than the true value) and you can’t compensate for them by taking additional data. Examples of Systematic Errors • If you forget to calibrate a balance or you’re off a bit in the calibration, all mass measurements will be high/low by the same amount. Some instruments require periodic calibration throughout the course of an experiment, so it’s good to make a note in your lab notebook to see whether the calibrations appears to have affected the data. • Another example is measuring volume by reading a meniscus (parallax).