Basic Concepts of Experimental Error

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Questions and Answers

What are systematic errors primarily caused by?

Random fluctuations in reading

The unique interpretation of data

Environmental conditions during measurement

Faulty calibration of instruments (correct)

Which type of error is characterized by consistently high or low readings due to user measurement techniques?

Parallax error (correct)

Determinate error

Zero error

Random error

How can systematic errors be reduced after they are detected?

By ignoring the error and relying on initial readings

Through statistical analysis of the data

By recalibrating the instrument or adjusting the data (correct)

By repeating the measurements multiple times

Which of the following statements is true regarding random errors?

They can be reduced by averaging multiple measurements. Signup and view all the answers

What is a primary characteristic of random errors?

They fluctuate above and below the true value. Signup and view all the answers

What is the main purpose of reporting accuracy and precision in experimental results?

To describe the reliability of the measurements. Signup and view all the answers

Which of the following methods can help reduce random errors?

Statistical analysis of outliers Signup and view all the answers

What does the number of significant figures in a measurement indicate?

The precision of the measurement Signup and view all the answers

What does experimental error refer to?

The difference between a measurement and the true value Signup and view all the answers

How is accuracy determined in measurements?

By a single measurement compared to the true value Signup and view all the answers

What does precision refer to?

The closeness of a group of measurements to each other Signup and view all the answers

Which type of experimental error affects the accuracy of measurements?

Systematic errors Signup and view all the answers

What is an example of precision in measurements?

Obtaining the same measurement over several trials Signup and view all the answers

What happens if a measurement is subject to systematic errors?

The results will consistently differ from the true value Signup and view all the answers

Which statement correctly distinguishes accuracy from precision?

Accuracy is about closeness to the accepted value, while precision is about closeness of repeated measurements Signup and view all the answers

How can systematic errors be addressed?

By calibrating the measurement instrument Signup and view all the answers

How many significant figures are in the number 13.20?

4 Signup and view all the answers

Which digit in the number 0.0034 is considered significant?

Both B and C Signup and view all the answers

What is the least number of significant figures in the calculation 22.37 cm x 3.10 cm x 85.75 cm?

3 Signup and view all the answers

How would the result of 5946.50525 cm³ be rounded to maintain the correct significant figures?

5940 cm³ Signup and view all the answers

Which of the following has the highest number of significant figures?

1000.0 Signup and view all the answers

What kind of zeroes do not count as significant figures?

Leading zeros Signup and view all the answers

When multiplying quantities, what dictates the number of significant figures in the result?

The least number of significant figures in any measurement Signup and view all the answers

In the number 1.007, how many significant figures are present?

4 Signup and view all the answers

What should the final answer be when adding 3.76 g, 14.83 g, and 2.1 g?

20.7 g Signup and view all the answers

Which rule is used when rounding 12.51?

Round up to 13 Signup and view all the answers

What is the percent error if the measured length of a wire is 4.25 cm and the true value is 4.08 cm?

4.17 % Signup and view all the answers

When rounding the number 12.4, what will be the result?

12 Signup and view all the answers

What happens when rounding the number 11.5?

It rounds to 12 Signup and view all the answers

Which of the following best defines 'Mean' in statistics?

The average of a set of data Signup and view all the answers

If a measurement shows 2.5555 and needs to be rounded to two decimal places, what is the result?

2.56 Signup and view all the answers

How is percent error expressed mathematically?

(Measured value - True value) / True value x 100 Signup and view all the answers

What is the mean of the numbers 6, 11, and 7?

8 Signup and view all the answers

What does a low standard deviation indicate about a set of data?

The numbers are very close to the average. Signup and view all the answers

Which step is NOT involved in calculating standard deviation?

Square the mean. Signup and view all the answers

How should experimental results be reported according to the content provided?

Mean plus standard deviation is reported. Signup and view all the answers

What can straight line graphs be used for?

To display trends and make predictions. Signup and view all the answers

What is the formula to report a measured quantity?

x = X ± S.D. Signup and view all the answers

In the context of standard deviation, what does S represent?

Standard deviation. Signup and view all the answers

What is the first step in the process of finding standard deviation?

Find the mean. Signup and view all the answers

What does the variable 'm' represent in the equation of a straight line?

slope Signup and view all the answers

Which of the following is a base unit in the International System of Units (SI)?

Kilogram Signup and view all the answers

What is the derived SI unit for pressure?

Pascal Signup and view all the answers

Which unit is used to measure velocity in SI units?

m/s Signup and view all the answers

Which of the following represents the expression for area in derived SI units?

Length² Signup and view all the answers

What is the SI unit for energy?

Joule Signup and view all the answers

How is acceleration expressed in SI units?

m/s² Signup and view all the answers

Which of the following symbols represents the unit for electric current?

A Signup and view all the answers

Study Notes

Basic Concepts

Experimental error is the difference between a measurement and the true value or between two measured values.
Experimental error is demonstrated by accuracy and precision.
Accuracy of a measurement refers to how close the measured value is to the true or accepted value.
Precision refers to how close together a group of measurements are to each other.
Precision has nothing to do with the true value of a measurement
Precision is sometimes referred to as repeatability or reproducibility.
A highly reproducible measurement gives values close to each other.
Accuracy can be determined by a single measurement.
Precision can only be determined with multiple measurements.

Types of Experimental Errors

Experimental errors are not mistakes in calculations or miscalculations.
Systematic errors affect the accuracy of a measurement.
Systematic errors are one-sided.
Repeated measurements yield results that differ from the true or accepted value by the same amount
Systematic errors cannot be improved by repeating measurements
Systematic errors are difficult to detect but can be reduced by refining measurement method or technique.
Random errors affect the precision of a measurement.
Random errors are two-sided errors.
Repeated measurements fluctuate above and below the true value.
Random errors are easily analyzed by statistical analysis.
Random errors can be reduced by refining the measurement method or technique.

Causes of Systematic Error

Faulty calibration of measuring instruments or poorly maintained instruments can cause systematic error.
Faulty reading of instruments by the user, also called parallax error. This consistently gives high or low readings
"Zero error" occurs when an instrument gives a reading when the true reading is zero.
Systematic errors can be reduced by recalibrating the instrument or subtracting/adding an error value to data
Taking more measurements does not reduce systematic error

Causes of Random Error

Unpredictable fluctuations in the readings of measurement apparatus.
The experimenter's interpretation of the instrumental reading.
Random errors can be reduced by repeating measurements several times and taking the average.
Statistical analysis can be used to analyze random errors.

Calculating Experimental Error

Reporting experimental results should describe accuracy and precision of the experimental measurements.
Significant figures estimate the precision of a measurement. The number of significant figures is the number of figures that are known with some degree of reliability.
The number 13.2 has 3 significant figures, 13.20 has 4.

Rules for Significant Digits

All non-zero digits are significant.
Zeros: leading zeros are not significant, captive zeros are significant, trailing zeros are significant only if the number contains a decimal point
When multiplying or dividing, the answer should have as many significant digits as the measurement with the fewest significant digits.
When adding or subtracting, the answer should have as many decimal places as the measurement with the fewest decimal places.

Rules for Rounding Off Numbers

If the digit to be dropped is greater than 5, the last retained digit is increased by 1.
If the digit to be dropped is less than 5, the last retained digit remains the same.
If the digit to be dropped is 5, and there are other non-zero digits following it, the last retained digit is increased by 1.
If the digit to be dropped is 5, and only zeroes follow it, the last retained digit is increased by 1 if it is odd, but remains the same if even.

Percent Error

Percent error measures the accuracy of a measurement.
% Error = [(Measured value - True value)/ True value] x 100

Mean and Standard Deviation

Mean is the average of a set of data.
Mean = sum of data points / number of data points
Standard deviation tells how spread out measurements are from the average.
A low standard deviation means measurements are close to the average, while a high standard deviation means measurements are spread out from the average

Reporting the Results of an Experimental Measurement

The result of an experimental measurement should be reported with two parts:
- Best estimate of measurement (e.g. mean)
- Variation of the measurements (e.g. standard deviation of the measurements)
- Measured quantity = x ± standard deviation

Straight Line Graphs

Straight line graphs display data variables and trends clearly, aiding in predictions.
They can display multiple dependent variables against one independent variable.
Equation of a straight line: A = mB + c, where m is slope, and c is y-intercept

SI Units

SI units has seven base quantities and base units
Quantities such as length, mass, time, temperature, amount of substance, electric current, luminous intensity can be derived.
There are derived SI units whose expressions can be calculated using seven base units. For example, Area = Length x Length, Velocity = Distance/time.

SI Prefixes

SI prefixes are used to represent multiples or submultiples of a unit.

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Description

This quiz covers the fundamental concepts of experimental error, focusing on accuracy and precision. It distinguishes between the two types of errors and explains their implications in measurements. Test your understanding of these crucial experimental principles.