Measurements and Errors Flashcards
Name all quantities and their fundamental base units
Time - seconds Mass - kilograms Length - metres Current - amperes Temperature - kelvin Intensity - candela Amount of substance - mole
Dimension
type of quantity independent of its units or value, e.g. time, length, mass etc.
Name all prefixes in standard form
tera (T) = x10^12 giga (G) = x10^9 mega (M) = x10^6 kilo (k) = x10^3 centi (c) = x10^2 milli (m) = x10^-3 micro (μ) = x10^-6 nano (n) = x10^-9 pico (p) = x10^-12 femto (f) = x10^15
Random Errors
- unpredictable (out of your control)
- present when any measurement is taken
- cannot be corrected
Suggest how to reduce the effect of random error on an investigation
- taking repeat measurements
- calculating a mean
Systematic Error
- readings differ from true value by consistent amount each time a measurement is taken
- arise from environment, methods of observation + uncalibrated measuring instruments
Suggest how to reduce the effect of systematic error on an investigation
- CANNOT carry out simple repeats
- must change technique or measuring instruments based on error suspected then repeat
How do random and systematic errors affect accuracy and precision
- random errors produce imprecise data
- systematic errors produce inaccurate data which may still be precise
Anomalies
- outliers (considerably outside of range)
- judged as not part of variation caused by random uncertainty
- excluded from data since results in invalid conclusion
Calibration
- establishing relationship between values recorded by measuring instruments and standard reference values
- calibration curve plotted
Repeatable
measurement is repeatable if investigation is repeated using same method and equipment to obtain same results
Reproducible
measurement is reproducible if investigation is repeated using different equipment and techniques to obtain same result
Accuracy
close to true value
Precision
little spread around mean dependent only on random errors
Suggest how to quote uncertainty of measurement
- uncertainty of a reading (one judgment) is half resolution of instrument
- uncertainty of measurement (two judgments) is resolution of instrument
- round uncertainty to same number of decimal places as measurement itself
Suggest how to find uncertainty of repeat measurements
mean value has uncertainty of half the range of measured values
Describe how to draw error bars on a graph
- plot mean values
- calculate range from repeats (ignoring anomalies)
- add error bars with lengths half the range on either side of data point
Describe how to determine uncertainties for gradients and y intercepts
- draw ‘best’ line of best fit
- draw dashed steepest/shallowest gradient possible
- % uncertainty = (best gradient - worst gradient)/best gradient x 100
- y intercept uncertainty found with same method
Suggest how to combine percentage uncertainties when adding or subtracting values
add absolute uncertainties
Suggest how to combine percentage uncertainties when multiplying or dividing values
add percentage uncertainties
Suggest how to calculate percentage uncertainty when raising a value to a power
multiply percentage uncertainty by the power
Suggest how data and graphs can be manipulated to determine the relationship between two variables
- plot graph of y against x
- if graph is not linear then square, cube or square root y and plot graphs
- the straightest line graph suggests the relationship between x and y
Zero Error
- measuring system gives false reading when true value of measured quantity is zero
- may result in systematic error
