Internal Assessment 2 Data Handling

1
Internal Assessment 2Data Handling

• Breithaupt parts of chapters 14.1, 14.2, 14.4
  16.1
• pages 218 to 220, 223 to 225 233

2
Significant figures

• Consider the number 3250.040
• It is quoted to SEVEN significant figures
• 3250.04 is SIX s.f.
• 3250.0 is FIVE s.f.
• 3250 is FOUR s.f. (NOT THREE!)
• 325 x 101 is THREE s.f. (as also is 3.25 x 103)
• 33 x 102 is TWO s.f. (as also is 3.3 x 103)
• 3 x 103 is ONE s.f. (3000 is FOUR s.f.)
• 103 is ZERO s.f. (Only the order of magnitude)

3
Complete the table below
4
Answers
5
Results tables
Headings should be clear Physical quantities
should have units All measurements should be
recorded (not just the average)
6
Reliabilty and validity of measurements

• Reliable
• Measurements are reliable if consistent values
  are obtained each time the same measurement is
  repeated.
• Reliable 45g 44g 44g 47g 46g
• Unreliable 45g 44g 67g 47g 12g 45g

• Valid
• Measurements are valid if they are of the
  required data OR can be used to obtain a required
  result
• For an experiment to measure the resistance of a
  lamp
• Valid current through lamp 5A p.d. across
  lamp 10V
• Invalid temperature of lamp 40oC colour of
  lamp red

7
Range and mean value of measurements

• Range
• This equal to the difference between the highest
  and lowest reading
• Readings 45g 44g 44g 47g 46g 45g
• Range 47g 44g
• 3g

• Mean value lt x gt
• This is calculated by adding the readings
  togetherand dividing by the number of readings
• Readings 45g 44g 44g 47g 46g 45g
• Mean value of mass ltmgt (454444474645) / 6
• ltmgt 45.2 g

8
Systematic and random errors

• Suppose a measurement should be 567cm
• Example of measurements showing systematic error
  585cm 583cm 584cm 586cm
• Systematic errors are often caused by poor
  measurement technique or incorrectly calibrated
  instruments.
• Calculating a mean value will not eliminate
  systematic error.

• Zero error can occur when an instrument does not
  read zero when it should do so. If not corrected
  for, zero error will cause systematic error. The
  measurement examples opposite may have been
  caused by a zero error of about 18 cm.
• Example of measurements showing random error
  only 566cm 568cm 564cm 567cm
• Random error is unavoidable but can be
  minimalised by using a consistent measurement
  technique and the best possible measuring
  instruments.
• Calculating a mean value will reduce the effect
  of random error.

9
Accuracy and precision of measurements

• Accurate
• Accurate measurements are obtained using a good
  technique with correctly calibrated instruments
  so that there is no systematic error.
• Precise
• Precise measurements are those that have the
  maximum possible significant figures. They are as
  exact as possible.

• The precision of a measuring instrument is equal
  to the smallest possible non-zero reading it can
  yield.
• The precision of a measurement obtained from a
  range of readings is equal to half the range.
• Example If a measurement should be 3452g
• Then 3400g is accurate but not precise
• whereas 4563g is precise but inaccurate

10
Uncertainty or probable error

• The uncertainty (or probable error) in the mean
  value of a measurement is half the range
  expressed as a value
• Example If mean mass is 45.2g and the range is
  3g then
• The probable error (uncertainty) is 1.5g
• Uncertainty is normally quoted to ONE significant
  figure (rounding up) and so the uncertainty is
  now 2g
• The mass might now be quoted as 45.2 2g
• As the mass can vary between potentially 43g and
  47g it would be better to quote the mass to only
  two significant figures
• So mass 45 2g is the best final statement
• NOTE The uncertainty will determine the number
  of significant figures to quote for a measurement

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Uncertainty in a single readingOR when
measurements do not vary

• The probable error is equal to the precision in
  reading the instrument
• For the scale opposite this would be
• 0.1 without the magnifying glass
• 0.02 perhaps with the magnifying glass

12
Percentage uncertainty

• It is often useful to express the probable error
  as a percentage
• percentage uncertainty probable error x 100
  
  measurement
• Example Calculate the uncertainity the mass
  measurement 45 2g
• percentage uncertainty 2g x 100
  
  45g
• 4.44

13
Combining uncertainties

• Addition or subtraction
• Add probable errors together, examples
• (56 4m) (22 2m) 78 6m
• (76 3kg) - (32 2kg) 44 5kg
• Multiplication or division
• Add percentage uncertainties together, examples
• (50 5m) x (20 1m) (50 10) x (20 5)
  1000 15 1000 150 m2
• (40 2m) (2.0 0.2s) (40 5) (2.0
  10) 20 15 20 1.5 ms-2
• Powers
• Multiply the percentage uncertainty by the power,
  examples
• (20 1m)2 (20 5)2 (202 (2 x 5))
  (400 10) 400 40 m2
• v(25 5 m2) v(25 20) v(25 (0.5 x
  20)) (5 10) 5 0.5 m

14
Notes from Breithaupt pages 219 to 220, 223 to
225 233

• Define in the context of recording measurements,
  and give examples of, what is meant by (a)
  reliable (b) valid (c) range (d) mean
  value (e) systematic error (f) random error
  (g) zero error (h) uncertainty (i) accuracy
  (j) precision and (k) linearity
• What determines the precision in (a) a single
  reading and (b) multiple readings?
• Define percentage uncertainty.
• Two measurements P 2.0 0.1 and Q 4.0 0.4
  are obtained. Determine the uncertainty (probable
  error) in (a) P Q (b) Q P (c) P x Q
  (d) Q / P (e) P3 (f) vQ.
• Measure the area of a piece of A4 paper and state
  the probable error (or uncertainty) in your
  answer.
• State the number 1230.0456 to (a) 6 sf, (b) 3 sf
  and (c) 0 sf.