Uncertainty 2 Flashcards
Percentage uncertainty of measurement =
(uncertainty )/value x 100%
Percentage uncertainty of repeated measurement
(uncertainty )/(mean value) x 100%
size of real object =
size of real object= (size of image)/magnification
Uncertainty =
half the range +/- mean value
Percentage uncertainty of graph
percentage uncertainty= |best gradient (gradient of line of best fit)-worst gradient (steepest/shallowest gradient of line of best fit)|/(best gradient) × 100%
Percentage uncertainty of y-intercept
percentage uncertainty= |best y intercept-worst y intercept|/(best y intercept) × 100%
Uncertainty of ruler
When measuring length, two uncertainties must be included: the uncertainty of the placement of the zero of the ruler and the uncertainty of the point the measurement is taken from. As both ends of the ruler have a ±0.5 scale division uncertainty, the measurement will have an uncertainty of ±1 division. For most rulers, this will mean that the uncertainty in a measurement of length will be ±1 mm.
Uncertainty from sig figs
one unit of lowest decimal place e.g. if value is 123.456
then uncertainty is +/- 0.001
Temperature is measured in
Kelvin
1W =
1 J/s
Micrometers give readings to within (What is the precision)
0.01mm
A digital micrometer gives a read-out equal to the
width of the micrometer gap
How do micrometers work
An analogue micrometer has a barrel on a screw thread with a pitch of 0.5mm – the edge of the barrel is marked in 50 equal intervals so each interval corresponds to changing the gap of the micrometer by 0.5/50mm = 0.01mm – the stem of the micrometer is marked with a linear scale graduated in 0.5mm marks – the reading of a micrometer is where the linear scale intersects the scale on the barrel. The linear scale + (barrel scale * 0.01)
How do vernier callipers
Vernier callipers are used for measurements of distances up to 100mm or more. Readings can be made to within 0.1mm. The sliding scale of an analogue vernier has ten equal intervals covering a distance of exactly 9mm so each interval of this scale is 0.1mm less than a 1mm interval. To make a reading – the zero mark on the sliding scale is used to read the main scale to the nearest millimetre. The reading is rounded down to the nearest millimetre. The mark on the sliding scale closest to a mark on the millimetre scale is located and its number noted. Multiplying this number by 0.1mm gives the distance to be added on the rounded-down reading
Accuracy
A measurement result is considered accurate if it is judged to be close to the true value.
Calibration
Marking a scale on a measuring instrument.
This involves establishing the relationship between indications of a measuring instrument and standard or reference quantity values, which must be applied.
Data
Information, either qualitative or quantitative, that have been collected.
Measurement error
The difference between a measured value and the true value.
Anomalies
These are values in a set of results which are judged not to be part of the variation caused by random uncertainty.
Random error
These cause readings to be spread about the true value, due to results varying in an unpredictable way from one measurement to the next.
Random errors are present when any measurement is made, and cannot be corrected. The effect of random errors can be reduced by making more measurements and calculating a new mean.
Systematic error
These cause readings to differ from the true value by a consistent amount each time a measurement is made.
Sources of systematic error can include the environment, methods of observation or instruments used.
Systematic errors cannot be dealt with by simple repeats. If a systematic error is suspected, the data collection should be repeated using a different technique or a different set of equipment, and the results compared.
Zero error
Any indication that a measuring system gives a false reading when the true value of a measured quantity is zero, eg the needle on an ammeter failing to return to zero when no current flows.
A zero error may result in a systematic uncertainty.
Evidence
Data that have been shown to be valid.
Fair test
A fair test is one in which only the independent variable has been allowed to affect the dependent variable.
Hypothesis
A proposal intended to explain certain facts or observations.
Interval
The quantity between readings eg a set of 11 readings equally spaced over a distance of 1 metre would give an interval of 10 centimetres.
Precision
Precise measurements are ones in which there is very little spread about the mean value.
Precision depends only on the extent of random errors – it gives no indication of how close results are to the true value.
Prediciton
A prediction is a statement suggesting what will happen in the future, based on observation, experience or a hypothesis.
Range
The maximum and minimum values of the independent or dependent variables;
Repeatable
A measurement is repeatable if the original experimenter repeats the investigation using same method and equipment and obtains the same results.
Reproducible
A measurement is reproducible if the investigation is repeated by another person, or by using different equipment or techniques, and the same results are obtained.
Resolution
This is the smallest change in the quantity being measured (input) of a measuring instrument that gives a perceptible change in the reading.
Sketch graph
A line graph, not necessarily on a grid, that shows the general shape of the relationship between two variables. It will not have any points plotted and although the axes should be labelled they may not be scaled.
True value
This is the value that would be obtained in an ideal measurement.
Uncertainty
The interval within which the true value can be expected to lie, with a given level of confidence or probability eg “the temperature is 20 °C ± 2 °C, at a level of confidence of 95 %”.
Validity
Suitability of the investigative procedure to answer the question being asked. For example, an investigation to find out if the rate of a chemical reaction depended upon the concentration of one of the reactants would not be a valid procedure if the temperature of the reactants was not controlled.
Valid conclusion
A conclusion supported by valid data, obtained from an appropriate experimental design and based on sound reasoning.
Categoric variables
Categoric variables have values that are labels eg names of plants or types of material or reading at week 1, reading at week 2 etc.
Continuous variables
Continuous variables can have values (called a quantity) that can be given a magnitude either by counting (as in the case of the number of shrimp) or by measurement (eg light intensity, flow rate etc).
Control variables
A control variable is one which may, in addition to the independent variable, affect the outcome of the investigation and therefore has to be kept constant or at least monitored.
Dependent variables
The dependent variable is the variable of which the value is measured for each and every change in the independent variable.
Independent variables
The independent variable is the variable for which values are changed or selected by the investigator.
Nominal variables
A nominal variable is a type of categoric variable where there is no ordering of categories (eg red flowers, pink flowers, blue flowers)
Variables
These are physical, chemical or biological quantities or characteristics.
