Formulas/Worded
What is "Precision" in terms of error in measurement?
"Precision" is the smallest unit on the measuring instrument.
If the 'relative error' of a measurement is 0.03, what is the 'percentage error?'
Percentage error
= 0.03 x 100%
= 3%
If:
Actual Value= 2.57kg
and the Measured Value= 2.5kg,
What is the 'Absolute Error?'
2.57kg-2.5kg
= 0.07kg or 70grams
How do you calculate upper and lower bounds for given measurements?
Measurement (+-) the absolute error.
What is 'absolute error' and how is it calculated?
Absolute error is the difference between the actual value and measured value. OR it is half the precision.
Absolute Error= Actual Value - Measured Value
If aboslute error= 0.015kg and actual value= 2.467kg, calculate the relative error to 3 decimal places.
Relative error= 0.006
On a 30cm ruler, the smallest unit of measurement is 1mm, hence, what is the 'absolute error?'
Absolute error= 0.5mm
If a pencil case is measured to be 25cm long and the absolute error is 0.5cm. What is the upper bound?
= 25.5cm
What is the difference between 'relative error' and 'percentage error?'
How they are expressed.
Relative error=decimal
Percentage error= written as a percentage
From the previous question, valued at 200 points, from the relative error of that question, now calculate the percentage error to 1 decimal place
Percentage Error= 0.6%
Absolute error= 0.025seconds
If the 'precision' of a measurement instrument is 5cm, what valued is used in order to find the upper/lower bounds
5cm divided by 2= 2.5cm. It is then added/subtracted from the actual measurement.
How are the upper/lower bounds of a measurement calculated?
Measurement (+/-) the absolute error
Calculate the 'percentage error' if the actual value of a measurement is 3.752cm and the absolute error is 0.014mm to 2 decimal places.
Percentage error
= (0.014/3.752) x 100
=0.37%
If the actual weight of a bag of grapes is 457grams, but the recorded weight is 450 grams, what is the absolute error?
Absolute error
= 457g-450g
= 7g
Explain what is meant by 'the upper and lower bounds' of a measurement?
Teacher's opinion
Name 3 possible sources of error when using measuring instruments?
Teachers opinion.
If the percentage error of a measurement is 0.7258%, what is the relative error, to 3 decimals places?
Relative Error= 0.007258
Answer: False, because the absolute error is half the precision and hence is 0.5 seconds.
If a book is measured to be 27cm long, using the 'precision,' calculate the upper and lower bounds.
Precision= 1cm
Upper Bound= 27.5cm
Lower Bound= 26.5cm