Uncertainty in a reading: ± half the smallest division
Uncertainty in a measurement: at least ±1 smallest division
Repeated Data Uncertainty: mean ± (range)/2
Combining uncertainties:
Adding / subtracting data = Add the absolute uncertainties
Multiplying/dividing data = Add the percentage uncertainties
Raising to a power = Multiply the percentage uncertainty by the power
Percentage Uncertainty: uncertainty/value x 100
Percentage uncertainty:
(Best Gradient - Worst Gradient)/Best Gradient x 100%
(Best y-intercept - Worst y-intercept)/Best y-intercept x 100%
Absolute uncertainty: uncertainty given as a fixed quantity
Fractional uncertainty: uncertainty given as a fraction of the measurement
Percentage uncertainty: uncertainty as a percentage of the measurement
To reduce percentage and fractional uncertainties, you need to measure larger quantities
Random errors:
affects precision --> causes differences in measurements and a spread about the mean
cannot get rid of all random errors
Reducing random errors:
Take at least 3 repeats and calculate a mean - allowing for anomalies to be identified
Use computers/data loggers to reduce human error and enable smaller intervals
Use appropriate equipment (e.g. a micrometer has a higher resolution [0.1mm] than a ruler [1mm])
Reducing systematic errors:
Calibrate apparatus by measuring a known value, if the reading is inaccurate then the systematic error is easily identified
In radiation experiments, correct for the background radiation by measuring it beforehand and excluding it from the final results
Read the meniscus (the central curve on the surface of a liquid) at eye level to reduce parallax error and use controls in experiments
Precision: Precise measurements are consistent, they fluctuate slightly about a mean value - this doesn’t indicate the value is accurate
Repeatability: If the original experimenter can redo the experiment with the same equipment and method then get the same results it is repeatable
Reproducibility: If the experiment is redone by a different person or with different techniques and equipment and the same results are found, it is reproducible
Resolution: The smallest change in the quantity being measured that gives a recognisable change in reading
Accuracy: A measurement close to the true value is accurate
Systematic errors:
Affect accuracy
Occurs due to the apparatus or faults in the experimental method
Systematic errors cause all results to be too high or too low by the same amount each time
i.e. a balance that isn't zeroed correctly (zero error) or reading a scale at a different angle (parallax error)
Types of data:
Discrete: only certain values can be taken, e.g. number of objects. Display on scatter graphs and bar charts
Continuous: can take any value on a scale e.g. current in a circuit. Display on line or scatter graph
Categoric: values that can be sorted into categories e.g. types of material. Display on a pie or bar chart
Ordered: data that can be put in ordered categories e.g. low, medium, high. Bar charts can display ordered data