Error in Measurements: Confused?

In summary, the conversation discusses the confusion surrounding determining the error in taking a reading for different types of measurements. It is clarified that for measurements with equal random uncertainties and no systematic uncertainties, the error can be calculated by adding all measurements and dividing by the number of measurements, and then dividing the uncertainty of one measurement by the square root of the number of measurements. This method is not applicable for root mean square calculations.
  • #1
gladius999
60
0
This has been very comfusing. Is the error in taking a reading the smallest or half the smallest division? Say a standard 30cm ruler, you can judge to nearest 0.5mm but since you take 2 readings you need to double the error. But then in titrations using a lab burette you count the titre as half the smallest division? I am very confused here as I cannot decide what to put when a question in an exam asks for the error in the reading.
 
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  • #2
For measurements of this type, where all the random uncertainties (not errors!) are equal and there are no systemantic uncertainties:
For n measurements:
Add all the measurements and divide by n to get average (don't use rms here).
Divide the uncertainty of one measurement by sqrt(n) to get the uncertainty of the average.
Bob S
 
  • #3

It is understandable that you are confused about the error in measurements, as there are different conventions for determining and expressing errors in different types of measurements. It is important to understand the specific guidelines and conventions for the type of measurement you are making in order to accurately determine and report the error.

In the case of a standard 30cm ruler, the smallest division is likely 1mm. When taking a reading, the error would be considered the smallest division, or 1mm in this case. However, since you are taking two readings (one at the start and one at the end), the total error would be double, or 2mm.

In titrations using a lab burette, the convention is to count the titre as half the smallest division. This is because the burette allows for more precise measurements and the smallest division may be smaller than 1mm. In this case, the error would be half of the smallest division.

When a question asks for the error in a reading, it is important to determine which convention to use based on the type of measurement being made. If it is a ruler or other measuring tool with larger divisions, the error would be the smallest division. If it is a more precise tool, such as a burette, the error would be half the smallest division.

In summary, the error in a reading can vary depending on the type of measurement and the conventions for determining and expressing errors. It is important to understand and follow the specific guidelines for the type of measurement being made in order to accurately determine and report the error.
 

Related to Error in Measurements: Confused?

1. What is measurement error?

Measurement error refers to the difference between the actual value of a quantity and the value that is measured or recorded. It is a common occurrence in scientific experiments and can be caused by various factors such as equipment limitations, human error, and environmental conditions.

2. How do you calculate measurement error?

To calculate measurement error, you need to know the actual or true value of the quantity being measured and the measured value. The measurement error is then calculated by subtracting the measured value from the actual value and dividing the result by the actual value. This value is then expressed as a percentage or absolute value.

3. What are the types of measurement error?

There are two types of measurement error: systematic error and random error. Systematic error is a consistent bias in the measurement that occurs due to faulty equipment or incorrect measurement techniques. Random error, on the other hand, is caused by unpredictable factors and can be reduced by taking multiple measurements and calculating an average.

4. How can measurement error affect the validity of results?

Measurement errors can significantly impact the validity of results by introducing inaccuracies and uncertainties. A large measurement error can lead to incorrect conclusions and affect the overall reliability of the data. It is important to minimize and account for measurement errors in order to obtain accurate and valid results.

5. How can measurement error be reduced or eliminated?

Measurement error can be reduced or eliminated by using proper measurement techniques, calibrating equipment regularly, and taking multiple measurements to calculate an average. It is also important to identify and control for any potential sources of error in the experimental setup. Additionally, using more precise and accurate equipment can also help reduce measurement errors.

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