What are precise measurements?

Precise measurements have very little spread about the mean value, i.e. they are close to each other .

What are accurate measurements?

Accurate measurements are close to the true value .

How do random errors arise?

Random errors arise from unpredictable fluctuations in an instrument’s readings due to uncontrollable factors, affecting the precision of measurements.

How do systematic errors arise?

Systematic errors arise from faulty instruments or flaws in the experimental method, affecting the accuracy of measurements.

What is a zero error ?

A zero error is a type of systematic error that occurs when an instrument gives a reading when the true reading is zero.

True or False? Zero errors affect the precision of measurements.

False. Zero errors are a type of systematic error, so they affect the accuracy of measurements, not precision.

Reliability is a measure of the ability of an experimental procedure to produce the expected results when using the same method and equipment.

Validity is a measure of the suitability of an experimental procedure to measure what it is intended to measure.

How can random errors be reduced?

Random errors can be reduced by repeating measurements several times and calculating an average using a device with smaller measuring intervals

How can systematic errors be reduced?

Systematic errors can be reduced by recalibrating instruments or using different instruments making corrections or adjustments to the technique

If a length is measured as 15.3 ± 0.2 cm, what is the absolute uncertainty in the measurement?

The absolute uncertainty in the measurement is ± 0.2 cm . length = 15.3 ± 0.2 cm measurement = 15.3 cm absolute uncertainty = ± 0.2 cm

How do you find the uncertainty in a reading ?

The uncertainty in a reading is ± half the smallest division.

How do you find the uncertainty in a measurement ?

The uncertainty in a measurement is at least ±1 smallest division.

How do you find the uncertainty of a set of readings ?

The uncertainty in a set of readings is half the range, or ± ½ (largest - smallest value).

True or False? When adding or subtracting data, the combined uncertainty is the sum of their percentage uncertainties.

False. When adding or subtracting data, the combined uncertainty is the sum of their absolute uncertainties.

True or False? When multiplying or dividing data, the combined uncertainty is the sum of their fractional or percentage uncertainties.

True. When multiplying or dividing data, the combined uncertainty is the sum of their fractional or percentage uncertainties.

What is the rule for propagating the uncertainty of a quantity which is raised to a power?

When a quantity is raised to a power, multiply the fractional or percentage uncertainty by the power.

If two measured lengths, 12.3 ± 0.2 cm and 7.8 ± 0.1 cm, are added together, what is their combined uncertainty?

Combined uncertainty = 0.2 cm + 0.1 cm = 0.3 cm When adding data, the combined uncertainty is the sum of their absolute uncertainties.

Find the percentage uncertainty in speed when dividing a distance measurement 4.5 m ± 2% by a time measurement 1.2 s ± 1%.

Percentage uncertainty in speed = 2% + 1% = 3% . When dividing data, the combined uncertainty is the sum of the percentage uncertainties.

What do error bars show on a graph?

Error bars are lines drawn above and below (or from side to side of) a point on a graph to show the absolute uncertainty of that measurement.

True or False? Error bars on a graph must all be the same size.

False. Error bars on a graph can have different sizes as they represent different uncertainties for each data point.

Define a line of best fit .

A line of best fit is a line that passes as close to all plotted points as possible on a graph.

What is the difference between a 'best' and 'worst' line of best fit?

A 'best' line of best fit is a line that passes as close to all plotted points as possible on a graph. A 'worst' line of best fit is either the steepest or shallowest possible line that fits within all the error bars on a graph.

What is percentage difference?

Percentage difference is an indication of how close the experimental value is to the accepted value.

True or False? The smaller the percentage difference, the greater the accuracy of the results of the experiment.

True. The smaller the percentage difference, the greater the accuracy of the results of the experiment.

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Processing Uncertainties (DP IB Physics)

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What are precise measurements?
Precise measurements have very little spread about the mean value, i.e. they are close to each other.
What are accurate measurements?
Accurate measurements are close to the true value.
How do random errors arise?
Random errors arise from unpredictable fluctuations in an instrument’s readings due to uncontrollable factors, affecting the precision of measurements.
How do systematic errors arise?
Systematic errors arise from faulty instruments or flaws in the experimental method, affecting the accuracy of measurements.
What is a zero error?
A zero error is a type of systematic error that occurs when an instrument gives a reading when the true reading is zero.
True or False?
Zero errors affect the precision of measurements.
False.
Zero errors are a type of systematic error, so they affect the accuracy of measurements, not precision.
Define reliability.
Reliability is a measure of the ability of an experimental procedure to produce the expected results when using the same method and equipment.
Define validity.
Validity is a measure of the suitability of an experimental procedure to measure what it is intended to measure.
How can random errors be reduced?
Random errors can be reduced by
- repeating measurements several times and calculating an average
- using a device with smaller measuring intervals
How can systematic errors be reduced?
Systematic errors can be reduced by
- recalibrating instruments or using different instruments
- making corrections or adjustments to the technique
If a length is measured as 15.3 ± 0.2 cm, what is the absolute uncertainty in the measurement?
The absolute uncertainty in the measurement is ± 0.2 cm.
- length = 15.3 ± 0.2 cm
- measurement = 15.3 cm
- absolute uncertainty = ± 0.2 cm
If a current is measured as 5.5 ± 0.1 A, what is the fractional uncertainty in the measurement?
The fractional uncertainty in the measurement is ± 0.02.
- current = 5.5 ± 0.1 A
- measurement = 5.5 A
- fractional uncertainty = $\frac{0.1}{5.5}$ = ± 0.02
If a mass is measured as 250 ± 5 g, what is the percentage uncertainty in the measurement?
The percentage uncertainty in the measurement is ± 2%.
- mass = 250 ± 5 g
- measurement = 250 g
- percentage uncertainty = $\frac{5}{250} \times 100 %$ = ± 2%
How do you find the uncertainty in a reading?
The uncertainty in a reading is ± half the smallest division.
How do you find the uncertainty in a measurement?
The uncertainty in a measurement is at least ±1 smallest division.
How do you find the uncertainty of a set of readings?
The uncertainty in a set of readings is half the range, or ± ½ (largest - smallest value).
True or False?
When adding or subtracting data, the combined uncertainty is the sum of their percentage uncertainties.
False.
When adding or subtracting data, the combined uncertainty is the sum of their absolute uncertainties.
True or False?
When multiplying or dividing data, the combined uncertainty is the sum of their fractional or percentage uncertainties.
True.
When multiplying or dividing data, the combined uncertainty is the sum of their fractional or percentage uncertainties.
What is the rule for propagating the uncertainty of a quantity which is raised to a power?
When a quantity is raised to a power, multiply the fractional or percentage uncertainty by the power.
If two measured lengths, 12.3 ± 0.2 cm and 7.8 ± 0.1 cm, are added together, what is their combined uncertainty?
Combined uncertainty = 0.2 cm + 0.1 cm = 0.3 cm
When adding data, the combined uncertainty is the sum of their absolute uncertainties.
Find the percentage uncertainty in speed when dividing a distance measurement 4.5 m ± 2% by a time measurement 1.2 s ± 1%.
Percentage uncertainty in speed = 2% + 1% = 3%.
When dividing data, the combined uncertainty is the sum of the percentage uncertainties.
A cylinder of volume $V = π r^{2} h$ has a radius of 5.0 ± 0.2 cm and a height of 10.0 ± 0.5 cm. Calculate the percentage uncertainty in the volume.
Percentage uncertainty in volume = 13%.
- $(\frac{∆ V}{V}) = 2 (\frac{∆ r}{r}) + (\frac{∆ h}{h})$
- $(\frac{∆ V}{V}) = 2 (\frac{0.2}{5.0}) + (\frac{0.5}{10.0}) = 0.13$
- percentage uncertainty = $0.13 \times 100 % = 13 %$
What do error bars show on a graph?
Error bars are lines drawn above and below (or from side to side of) a point on a graph to show the absolute uncertainty of that measurement.
True or False?
Error bars on a graph must all be the same size.
False.
Error bars on a graph can have different sizes as they represent different uncertainties for each data point.
Define a line of best fit.
A line of best fit is a line that passes as close to all plotted points as possible on a graph.
What is the difference between a 'best' and 'worst' line of best fit?
A 'best' line of best fit is a line that passes as close to all plotted points as possible on a graph.
A 'worst' line of best fit is either the steepest or shallowest possible line that fits within all the error bars on a graph.
State the equation for percentage uncertainty in gradient.
The equation for percentage uncertainty in gradient is:
- percentage uncertainty = $\frac{b e s t g r a d i e n t - w o r s t g r a d i e n t}{b e s t g r a d i e n t} \times 100 %$
What is percentage difference?
Percentage difference is an indication of how close the experimental value is to the accepted value.
State the equation for percentage difference.
The equation for percentage difference is:
- percentage difference = $\frac{e x p e r i m e n t a l v a l u e - a c c e p t e d v a l u e}{a c c e p t e d v a l u e} \times 100 %$
True or False?
The smaller the percentage difference, the greater the accuracy of the results of the experiment.
True.
The smaller the percentage difference, the greater the accuracy of the results of the experiment.
Draw the lines of maximum and minimum gradient on the graph.
The lines of maximum and minimum gradient on the graph are:

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