Which readings should be excluded when calculating a mean?

Anomalous readings should be excluded, as they are not representative of the true value and would distort the mean.

To how many significant figures should a calculated mean be quoted?

The same number of significant figures as the raw readings used to calculate it.

A student cannot directly measure the extension of a spring in a Hooke's law experiment. Explain how the extension is obtained for the data table.

Extension is calculated from two measured quantities, the initial length and final length of the spring, by subtracting one from the other.

When planning a data table, columns should be left not only for measured readings but also for any quantities that must be .......... from them, such as area from a measured radius.

When planning a data table, columns should be left not only for measured readings but also for any quantities that must be calculated from them, such as area from a measured radius.

True or False? Averaging repeat readings allows the mean to be quoted to more significant figures than the raw data.

False. The mean must be quoted to the same number of significant figures as the readings used to calculate it — averaging does not create extra precision.

Define a line of best fit .

A line of best fit is a line drawn through plotted points with an equal number of points above and below it. It is not forced through the origin unless the data supports this.

On which axis should the independent variable be plotted?

The x-axis . The dependent variable is plotted on the y-axis.

What is the convention for labelling a graph axis?

The quantity symbol and its unit , separated by a forward slash, e.g. F / N.

All values should be plotted precisely to within half a small .......... .

All values should be plotted precisely to within half a small square .

True or False? The ln and log functions on a calculator are the same, both working to base 10.

False. log works to base 10, but ln is log to the base e (the exponential function). An exponential equation should be linearised using ln, not log.

Define a derived unit .

A derived unit is a unit formed mathematically from combinations of the SI base units.

Derive the SI base units of the Pascal (Pa), given pressure = force ÷ area.

Pa = (kg m s -2 ) ÷ m 2 = kg m -1 s -2

The Joule (J), the unit of energy, has SI base units of .......... .

The Joule (J), the unit of energy, has SI base units of kg m 2 s -2 .

True or False? Refractive index has units, since it is calculated by dividing two speeds.

False. Refractive index is a ratio of two quantities with the same units, so the units cancel — it has no units .

How can the rate of change of a quantity be identified from a graph?

From the gradient of the graph — an increasing gradient shows an increasing rate of change, and a decreasing gradient shows a decreasing rate of change.

A directly proportional relationship is represented by a .......... graph passing through the origin.

A directly proportional relationship is represented by a straight-line graph passing through the origin.

True or False? Any straight-line graph shows a directly proportional relationship between the two variables.

False. A straight line only shows direct proportionality if it passes through the origin . A straight line with a non-zero y-intercept is linear but not directly proportional.

A quantity F and a distance d are related by an inverse square law. If d is tripled, by what factor does F change?

F decreases by a factor of 3 2 = 9 .

How should a gradient triangle be drawn to calculate a constant from a straight-line graph?

As large as possible — more than half the length of the line — using points that lie on the line of best fit , avoiding raw data points where possible.

What determines the units of a gradient calculated from a graph?

The ratio of the units of the y-variable to the units of the x-variable.

Before stating that two variables are directly or inversely proportional, you must check that any remaining variables in the equation are .......... .

Before stating that two variables are directly or inversely proportional, you must check that any remaining variables in the equation are constant .

True or False? Using a small gradient triangle with data points close together gives a more accurate gradient than using a large triangle.

False. A large gradient triangle, taking up more than half the line, reduces the effect of reading error and gives a more accurate gradient.

Precision is how close repeated measured values are to each other.

Accuracy is how close a measured value is to the true value .

How can the accuracy of a measurement be increased?

By repeating measurements and calculating a mean average.

What is the difference between the sensitivity and resolution of an instrument?

Resolution is the smallest change an instrument can observe (display); sensitivity is the smallest change it can detect .

The .......... is an estimate of the difference between a measurement reading and the true value.

The uncertainty is an estimate of the difference between a measurement reading and the true value.

True or False? A set of measurements can be precise without being accurate.

True. If every reading has the same systematic error , repeated readings can be close to each other (precise) while still being far from the true value (not accurate).

Define parallax error .

Parallax error is an error caused by reading a scale from an angle rather than perpendicular to it (at eye level), making the reading appear different from the true value.

Define fiducial marker .

A fiducial marker is a fixed reference point used to improve timing accuracy, for example marking the lowest point of a pendulum's swing so measurements are always taken from the same point.

How can the effect of random errors be reduced in an experiment?

By taking as many repeat readings as possible and calculating the average (mean) of the repeats.

Why should a fiducial marker for a pendulum be positioned at the lowest point of its swing rather than the highest point?

The pendulum moves fastest at its lowest point, giving the sharpest, most precise moment to start or stop timing, which reduces timing uncertainty.

True or False? Checking that an ammeter reads 0 A when no current flows is a way of reducing random error.

False. This checks for a zero error , which is a type of systematic error , not a random error.

To reduce unwanted heating effects in a circuit, the power supply should be .......... between readings.

To reduce unwanted heating effects in a circuit, the power supply should be turned off between readings.

Give two examples of poor experimental practice, other than failing to repeat readings, that increase error.

Any two from: Using equipment with poor precision/resolution (e.g. a ruler instead of a micrometer) Not checking for zero errors Not using a fiducial marker where appropriate Not checking equipment works properly beforehand Difficulty controlling variables (e.g. room temperature) Unwanted heating effects in circuits

A data logger is an electronic device that automatically monitors and records environmental parameters (e.g. temperature, pressure, voltage, current) over time, using sensors and a computer chip to store data.

Define a reproducible method.

A method is reproducible if it can be repeated, potentially with different equipment or materials, by other scientists and still produce the same or comparable results.

State three benefits of using data loggers instead of manual data collection.

Any three from: Higher accuracy Reduced human error (e.g. reaction time) Readings taken over long periods of time Readings taken over very short periods of time, too quick for humans Reduced safety risk in extreme conditions

How can a camera be used to improve an experiment where a scale changes too quickly to read directly?

A photo burst is taken during the experiment and the scale is read from the photos afterwards; if the frame rate or time of each photo is known, quantities such as velocity can be calculated.

True or False? Computer modelling can be used to speed up time to predict the future outcome of an experiment.

True. Computer modelling processes data (often from a data logger) using software to generate graphs and predictions faster than manual analysis.

Testing the same method used to find the resistivity of a constantan wire on a different material, such as copper, checks that the method is .......... .

Testing the same method used to find the resistivity of a constantan wire on a different material, such as copper, checks that the method is reproducible .

Define absolute uncertainty .

Absolute uncertainty is the uncertainty in a measurement given as a fixed quantity, in the same units as the measurement.

Define fractional uncertainty .

Fractional uncertainty is the uncertainty in a measurement given as a fraction of the measured value.

What is the uncertainty in a single reading from an analogue scale?

± half the smallest division (the resolution) of the instrument.

What is the uncertainty in repeated data?

Half the range, i.e. ± ½ (largest value − smallest value).

How are absolute uncertainties combined when adding or subtracting data?

The absolute uncertainties are added together.

True or False? The uncertainty in a constant such as π is taken to be zero.

True. Numbers and constants (e.g. π ) are treated as having zero uncertainty.

The uncertainty in a digital reading is taken as ± the .......... unless otherwise stated.

The uncertainty in a digital reading is taken as ± the last significant digit unless otherwise stated.

International A Level (IAL)PhysicsEdexcelFlashcards6. Practical Skills in Physics IIPractical Skills II: Analysis

Practical Skills II: Analysis (Edexcel International A Level (IAL) Physics): Flashcards

Exam code: YPH11

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FrontCalculations using Experimental Data
Define mean, in the context of repeat readings.

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Cards in this collection (63)

Define mean, in the context of repeat readings.
The mean is the sum of the repeat readings divided by the number of readings taken:
$mean = \frac{sum of readings}{number of readings}$
Which readings should be excluded when calculating a mean?
Anomalous readings should be excluded, as they are not representative of the true value and would distort the mean.
To how many significant figures should a calculated mean be quoted?
The same number of significant figures as the raw readings used to calculate it.
A student cannot directly measure the extension of a spring in a Hooke's law experiment. Explain how the extension is obtained for the data table.
Extension is calculated from two measured quantities, the initial length and final length of the spring, by subtracting one from the other.
When planning a data table, columns should be left not only for measured readings but also for any quantities that must be .......... from them, such as area from a measured radius.
When planning a data table, columns should be left not only for measured readings but also for any quantities that must be calculated from them, such as area from a measured radius.
True or False?
Averaging repeat readings allows the mean to be quoted to more significant figures than the raw data.
False.
The mean must be quoted to the same number of significant figures as the readings used to calculate it — averaging does not create extra precision.
Define a line of best fit.
A line of best fit is a line drawn through plotted points with an equal number of points above and below it. It is not forced through the origin unless the data supports this.
On which axis should the independent variable be plotted?
The x-axis. The dependent variable is plotted on the y-axis.
What is the convention for labelling a graph axis?
The quantity symbol and its unit, separated by a forward slash, e.g. F / N.
Explain why taking natural logs of the radioactive decay equation $N = N_{0} e^{- λ t}$ produces a straight-line graph.
Taking ln of both sides gives:
$\ln N = - λ t + \ln N_{0}$
This matches y = mx + c, so plotting ln N against t gives a straight line with gradient −λ and y-intercept ln N₀.
All values should be plotted precisely to within half a small ...........
All values should be plotted precisely to within half a small square.
True or False?
The ln and log functions on a calculator are the same, both working to base 10.
False.
log works to base 10, but ln is log to the base e (the exponential function). An exponential equation should be linearised using ln, not log.
Define a derived unit.
A derived unit is a unit formed mathematically from combinations of the SI base units.
Derive the SI base units of the Newton (N), given F = ma.
N = kg × m s^-2 = kg m s^-2
Derive the SI base units of the Pascal (Pa), given pressure = force ÷ area.
Pa = (kg m s^-2) ÷ m² = kg m^-1 s^-2
What is 1 dm³ equivalent to?
1 litre.
The Joule (J), the unit of energy, has SI base units of ...........
The Joule (J), the unit of energy, has SI base units of kg m² s^-2.
True or False?
Refractive index has units, since it is calculated by dividing two speeds.
False.
Refractive index is a ratio of two quantities with the same units, so the units cancel — it has no units.
Define directly proportional.
Two variables y and x are directly proportional ( $y \propto x$ ) when y increases at the same rate as x, represented by a straight-line graph through the origin.
Define inversely proportional.
Two variables y and x are inversely proportional ( $y \propto \frac{1}{x}$ ) when y decreases at the same rate that x increases, represented by a curve with decreasing gradient.
How can the rate of change of a quantity be identified from a graph?
From the gradient of the graph — an increasing gradient shows an increasing rate of change, and a decreasing gradient shows a decreasing rate of change.
What graph shape indicates that the dependent variable is constant as the independent variable changes?
A straight horizontal line.
A directly proportional relationship is represented by a .......... graph passing through the origin.
A directly proportional relationship is represented by a straight-line graph passing through the origin.
True or False?
Any straight-line graph shows a directly proportional relationship between the two variables.
False.
A straight line only shows direct proportionality if it passes through the origin. A straight line with a non-zero y-intercept is linear but not directly proportional.
Define an inverse square law relationship.
An inverse square law relationship ( $y \propto \frac{1}{x^{2}}$ ) is one where, if x increases by a factor of n, y decreases by a factor of n².
A quantity F and a distance d are related by an inverse square law. If d is tripled, by what factor does F change?
F decreases by a factor of 3² = 9.
How should a gradient triangle be drawn to calculate a constant from a straight-line graph?
As large as possible — more than half the length of the line — using points that lie on the line of best fit, avoiding raw data points where possible.
What determines the units of a gradient calculated from a graph?
The ratio of the units of the y-variable to the units of the x-variable.
Before stating that two variables are directly or inversely proportional, you must check that any remaining variables in the equation are ...........
Before stating that two variables are directly or inversely proportional, you must check that any remaining variables in the equation are constant.
True or False?
Using a small gradient triangle with data points close together gives a more accurate gradient than using a large triangle.
False.
A large gradient triangle, taking up more than half the line, reduces the effect of reading error and gives a more accurate gradient.
Define precision.
Precision is how close repeated measured values are to each other.
Define accuracy.
Accuracy is how close a measured value is to the true value.
How can the accuracy of a measurement be increased?
By repeating measurements and calculating a mean average.
What is the difference between the sensitivity and resolution of an instrument?
Resolution is the smallest change an instrument can observe (display); sensitivity is the smallest change it can detect.
The .......... is an estimate of the difference between a measurement reading and the true value.
The uncertainty is an estimate of the difference between a measurement reading and the true value.
True or False?
A set of measurements can be precise without being accurate.
True.
If every reading has the same systematic error, repeated readings can be close to each other (precise) while still being far from the true value (not accurate).
Define parallax error.
Parallax error is an error caused by reading a scale from an angle rather than perpendicular to it (at eye level), making the reading appear different from the true value.
Define fiducial marker.
A fiducial marker is a fixed reference point used to improve timing accuracy, for example marking the lowest point of a pendulum's swing so measurements are always taken from the same point.
How can the effect of random errors be reduced in an experiment?
By taking as many repeat readings as possible and calculating the average (mean) of the repeats.
Why should a fiducial marker for a pendulum be positioned at the lowest point of its swing rather than the highest point?
The pendulum moves fastest at its lowest point, giving the sharpest, most precise moment to start or stop timing, which reduces timing uncertainty.
True or False?
Checking that an ammeter reads 0 A when no current flows is a way of reducing random error.
False.
This checks for a zero error, which is a type of systematic error, not a random error.
To reduce unwanted heating effects in a circuit, the power supply should be .......... between readings.
To reduce unwanted heating effects in a circuit, the power supply should be turned off between readings.
Give two examples of poor experimental practice, other than failing to repeat readings, that increase error.
Any two from:
- Using equipment with poor precision/resolution (e.g. a ruler instead of a micrometer)
- Not checking for zero errors
- Not using a fiducial marker where appropriate
- Not checking equipment works properly beforehand
- Difficulty controlling variables (e.g. room temperature)
- Unwanted heating effects in circuits
Define data logger.
A data logger is an electronic device that automatically monitors and records environmental parameters (e.g. temperature, pressure, voltage, current) over time, using sensors and a computer chip to store data.
Define a reproducible method.
A method is reproducible if it can be repeated, potentially with different equipment or materials, by other scientists and still produce the same or comparable results.
State three benefits of using data loggers instead of manual data collection.
Any three from:
- Higher accuracy
- Reduced human error (e.g. reaction time)
- Readings taken over long periods of time
- Readings taken over very short periods of time, too quick for humans
- Reduced safety risk in extreme conditions
How can a camera be used to improve an experiment where a scale changes too quickly to read directly?
A photo burst is taken during the experiment and the scale is read from the photos afterwards; if the frame rate or time of each photo is known, quantities such as velocity can be calculated.
True or False?
Computer modelling can be used to speed up time to predict the future outcome of an experiment.
True.
Computer modelling processes data (often from a data logger) using software to generate graphs and predictions faster than manual analysis.
Testing the same method used to find the resistivity of a constantan wire on a different material, such as copper, checks that the method is ...........
Testing the same method used to find the resistivity of a constantan wire on a different material, such as copper, checks that the method is reproducible.
Define absolute uncertainty.
Absolute uncertainty is the uncertainty in a measurement given as a fixed quantity, in the same units as the measurement.
Define fractional uncertainty.
Fractional uncertainty is the uncertainty in a measurement given as a fraction of the measured value.
What is the uncertainty in a single reading from an analogue scale?
± half the smallest division (the resolution) of the instrument.
What is the uncertainty in repeated data?
Half the range, i.e. ± ½ (largest value − smallest value).
How are absolute uncertainties combined when adding or subtracting data?
The absolute uncertainties are added together.
True or False?
The uncertainty in a constant such as π is taken to be zero.
True.
Numbers and constants (e.g. π) are treated as having zero uncertainty.
The uncertainty in a digital reading is taken as ± the .......... unless otherwise stated.
The uncertainty in a digital reading is taken as ± the last significant digit unless otherwise stated.
How are percentage uncertainties combined when multiplying or dividing data?
The percentage (or fractional) uncertainties are added together.
How is the percentage uncertainty found when a measured quantity is raised to a power?
The percentage uncertainty is multiplied by the power.
Define percentage uncertainty.
$Percentage uncertainty = \frac{uncertainty}{measured value} \times 100 %$
For multiple (repeat) readings, what value is used as the uncertainty when calculating percentage uncertainty?
Half the range of the readings (the difference between the highest and lowest reading).
True or False?
Percentage uncertainty is expressed in the same units as the original measurement.
False.
Percentage uncertainties have no units — only the % sign.
A calculated percentage uncertainty should be quoted to at least one fewer .......... than the data, but no more than the number the data has.
A calculated percentage uncertainty should be quoted to at least one fewer significant figure than the data, but no more than the number the data has.
A student records repeat values of angular frequency, ω: 0.154, 0.153, 0.159, 0.147, 0.152 rad s^-1. Calculate the percentage uncertainty in the mean value.
Mean ω = 0.153 rad s^-1.
Half the range = ½ × (0.159 − 0.147) = 0.006 rad s^-1.
Percentage uncertainty = (0.006 ÷ 0.153) × 100% = 3.92%.

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