Uncertainty and error

1.2.7 Distinguish between precision and accuracy Accuracy is how close to the “correct” value Precision is being able to repeatedly get the same value Measurements are accurate if the systematic error is small Measurements are precise if the random error is small. Examples: groupings on targets

Example of precision and accuracy A voltmeter is being used to measure the potential difference across an electrical component. If the voltmeter is faulty in some way, such that it produces a widely scattered set of results when measuring the same potential difference, the meter would have low precision. If the meter had not been calibrated correctly and consistently measured 0.1V higher than the true reading (zero offset error), it would be in accurate.

1.2.6 Describe and give examples of random and systematic errors Explain how the effects of random errors may be reduced. There are two types of error, random and systematic. Random Errors - occur when you measure a quantity many times and get lots of slightly different readings. Examples - misreading apparatus, Errors made with calculations, Errors made when copying collected raw data to the lab report Can be reduced by repeating measurements many times. Measurements are precise if the random error is small

1.2.6 Describe and give examples of random and systematic errors Explain how the effects of random errors may be reduced. There are two types of error, random and systematic. Systematic error – when there is something wrong with the measuring device or method Examples – poor calibration, a consistently bad reaction time on the part of the recorder, parallax error Can be reduced by repeating measurements using a different method, or different apparatus and comparing the results, or recalibrating a piece of apparatus Measurements are accurate if the systematic error is small.

Graphs can be used to help us identify different types of error. Low precision is represented by a wide spread of points around an expected value. Low accuracy is represented by an unexpected intercept on the y-axis. Low accuracy gives rise to systematic errors.

Accurate or Precise?

1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figures The number of sig figs should reflect the precision of the value of the input data. If the precision of the measuring instrument is not known then as a general rule, give your answer to 3 sig figs. You may be penalized on the IB exam if you round your answer off to too few sig figs or if you give to many.

Three Basic Rules Non-zero digits are always significant has ____ significant figures Any zeros between two significant digits are significant has ____ significant figures A final zero or trailing zeros if it has a decimal, ONLY, are significant has ____ significant figures 200 has ____ significant figures

1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figures One rule: for multiplication and division, the number of significant digits in a result should not exceed that of the least precise value upon which it depends.

1.2.9 Practice 13(Dickinson) A meter rule was used to measure the length, height and thickness of a house brick and a digital balance was used to measure its mass. The following data were obtained. Length = 20.5cm, height = 8.4cm, thickness 10.2cm, mass = g Calculate the density of the house brick and give your answer to an appropriate number of sig figs.

1.2.9 Practice 13(Dickinson) Solution Density = (mass/volume) Density = ( / ) Density = g cm -3 Density = 1.8 g cm -3

State uncertainties as absolute, fractional and percentage uncertainties. Random uncertainties(errors) due to the precision of a piece of apparatus can be represented in the form of an uncertainty range. Experimental work requires individuals to judge and record the numerical uncertainty of recorded data and to propagate this to achieve a statement of uncertainty in the calculated results.

State uncertainties as absolute, fractional and percentage uncertainties. Rule of Thumb Analogue instruments = +/- half of the limit of reading  Ex. Meter stick’s limit of reading is 1mm so it’s uncertainty range is +/- 0.5mm Digital instruments = +/- the limit of the reading  Ex. Digital Stopwatch’s limit of reading is 0.01s so it’s uncertainty range is +/- 0.01s

We can express this uncertainty in one of three ways- using absolute, fractional, or percentage uncertainties  Absolute uncertainties are constants associated with a particular measuring device.  (Ratio) Fractional uncertainty = absolute uncertainty measurement  Percentage uncertainties = fractional x 100%

Example A meter rule measures a block of wood 28mm long. Absolute = 28mm +/- 0.5mm Fractional = 0.5mm = 28mm +/ mm Percentage = x 100% = 28mm +/- 1.79%

State uncertainties as absolute, fractional and percentage uncertainties. Random uncertainties(errors) due to the precision of a piece of apparatus can be represented in the form of an uncertainty range. Experimental work requires individuals to judge and record the numerical uncertainty of recorded data and to propagate this to achieve a statement of uncertainty in the calculated results.