Unit 11: Measurement and Data Processing ; Topic 11.1 & 11.2 Uncertainty & Error Flashcards
Flashcard Main Resource: https://sites.google.com/site/ibchemistryellesmerecollege/home/topic-11---measurement-data-processing/11-1-uncertainty-error https://docs.google.com/presentation/d/1bG82pSzkzmEQNXPHAPcgOogWW42Eaiy04BkBzKLV1nw/edit#slide=id.p19
Qualitative data is…
non-numerical data obtained from an experiment. These will be observations made during an experiment.
Quantitative data is…
numerical data
why do random errors arise?
due to the limitations of the measuring apparatus.
what else is random errors called?
human error
how are random errors determined?
it is determined by the experimenter’s skill or ability to perform the experiment and read scientific measurements.
what should all measurements be quoted with?
an uncertianty
what does the uncertainty indicate?
the size of the random error
what is an Analogue apparatus?
mechanical devices that indicate the magnitude of the quantity in the form of the pointer movement
when using an Analogue apparatus the uncertainty on a measurement is half of the what?
the smallest division that you take a reading to.
what is a Digital Instrument?
The instrument which represents the measured value in the form of the digital number
when using a digital instrument the uncertainty on a measurement is quoted as…
± the smallest division
what is an example of uncertainty with a reading taken with a 2-decimal place electronic balance? (digital instrument)
2.46 ± 0.01g.
if a voltmeter has an analogue scale and the smallest scale division is 1 volt, what is the uncertainty from reading this scale?
± 0.5 volts.
if a voltmeter has a digital scale that reads 13.8, What is the uncertainty from reading this scale? and how was that derived?
The uncertainty from reading this scale is ± 0.1 volts. This is because the least significant digit is the 8.
what does the effects of random uncertainties mean?
The effects of random uncertainties should mean that the measurements taken will be distributed on either side of the mean.
can random uncertainties be completely eliminated?
The random uncertainties can never be completely eliminated but the effect of random uncertainties can be reduced.
How can you reduce the effect of the random uncertainties?
by repeating the measurements more often.
what is a Systematic error?
Systematic errors are errors that affect the accuracy of a measurement.
how can a systematic error be introduced into an experiment?
A systematic error can be introduced into an experiment due to the apparatus used or the procedure.
are systematic errors are always in the same direction?
yes
how can the presence of systematic errors be identified?
by comparison with accepted literature values for quantities.
what do we use to compare the experimental value with the accepted literature value?
percentage error
what is the formula for percentage error?
= (experimental value – accepted value/accepted value) x 100
how do you know if the experiment involves some systematic errors?
If the percentage error is greater than the percentage uncertainty due to random errors
what happens if the percentage error is smaller than the percentage uncertainty
any deviation from the literature value can be explained in terms of random errors, that is, the limitations of the measuring apparatus.
what does precision relate to?
reproducibility of results, meaning that multiple measurements give nearly identical values.
what does high precision mean?
High precision means that repeat values are close together and close to the mean.
what does accuracy refer to?
how close a measurement is to the actual value of a particular quantity.
what is low accuracy due to?
Low accuracy is due to systematic errors within the experimental procedure.
how are random errors characterized in terms of precision and accuracy?
Random errors are characterized by high accuracy and low precision
how are systematic errors characterized in terms of precision and accuracy?
Systematic errors are characterized by high precision but low accuracy.
The uncertainty is usually quoted to how many significant figures?
one
how should the measurement be stated?
the measurement should be stated so that the uncertainty is in the last significant figure – no figures should be quoted after the uncertainty.
Consider a value of 1.735 ± 0.1 obtained from an equation, The uncertainty is in this decimal place, so no figures should be quoted beyond it. This quantity should then be quoted as…
1.7± 0.1.
what are the significant digits rules?
- All non-zero digits are significant.
- “Captive” zeros (zeros between non-zero digits) are significant.
- Leading zeros (zeros on the left) are never significant.
- Trailing zeros…
A). Are not significant if they are place holders(left of a decimal)
B). Are significant if they indicate a measurement (right of a decimal) - Exact numbers (counting numbers) have unlimited significant digits.
what are the rules for rounding off?
- If the digit to be removed:
A) is less than 5 the preceding digits stays the same.
B) is 5 or greater, the preceding number is increased by 1.
how do you add and subtract significant digits?
- Add up the digits by columns.
- Round off the final answer to the same number of decimal places as the least precise number.
how do you multiply and divide significant digits?
- Multiply the values as normal.
- Round off the final answer to the same number of significant digits as the least precise number.
Uncertainty’s may be reported in what 2 forms?
absolute value, eg. 1.23 ± 0.02m or as a percentage value, eg. 1.23m ± 2%
out of absolute and relative uncertainties which best fits with the statement “for any measuring device is the same for each measurement.”
Absolute Uncertainty
Absolute Uncertainty =
% Uncertainty / 100 x Value
For Example: if the final value of calculation is 23.27 ± 1%, the Absolute Uncertainty = 1/100 x 23.27 = 0.2
Therefore, final answer is…
23.27 ± 0.2
Percentage / Relative Uncertainty is the measure of the uncertainty with respect to what?
measure of the uncertainty with respect to the magnitude of the measurement.
how is Percentage / Relative Uncertainty expressed?
It is expressed as a % with 1 or 2 s.f
Percentage Uncertainty =
= Absolute uncertainty / Value x 100
When adding or subtracting measurements, we add the what uncertainty?
absolute
When multiplying or dividing measurements we add the what uncertainty?
relative/percentage
Eg. Calculate the absolute uncertainty when 9.78 ± 0.04 is divided by 3.349 ± 0.005 and quote the final answer to an appropriate number of significant figures.
Answer = 2.92 ± 0.02
Graphs are used extensively in science to show the relationship between two variables. Graphs may be either…
Sketched graphs, or Drawn graphs
sketched graphs are where…
the axes are labelled but there is no scale.
drawn graphs are where…
the axes are labeled and have scales.
what is the independent Variable?
What is changed in an experiment – what is being investigated.
what is the dependent Variable?
What is measured in an experiment.
Fill in the blanks:
The line of best fit must be a – line and pass through the – for a – relationship.
The line of best fit must be straight line and pass through the origin for a proportional relationship.
The gradient (slope) gives us an idea of what?
how much one quantity (the dependent variable) is affected by another quantity (the independent variable).
what happens If the gradient is large?
then a small change in the independent variable has a large effect on the dependent variable.
Gradient=
= Change in Y / change in X
The units of the gradient are obtained by…
dividing the units of the quantity on the y-axis by the units of the quantity on the x-axis.
what do you do to determine the gradient of a curve?
For a curve draw a tangent and determine the gradient of the tangent.
