n t easurement an ata rocess ngn easuremen an a a rocess ng
Learning outcomes:
- Distinguish between precision and accuracy
- Describe random uncertainties and systematic errors
- State random uncertainties as an uncertainty range
- Describe how effects of Random uncertainties can be reduced 
 11.2 Uncertainty in Calculate results
- State uncertainties as an absolute and a percentage uncertainty
- Determine the uncertainties in results
 
 graph behavior 
- Draw best fit lines through data points on a graph
- Determine the values of physical quantities from graphs
 
  Uncertainty in analogue instruments :
 Measuring ength with meter! smallest scale is " mm
so uncertainty is # $%& mm
 )ndicating the length of the marker could be "'%(& cm or "'%&&
 $%ample 1 :
 $%ample 2 :
 Measuring volume liquid in a cylinder! smallest scale is ' ml 
so uncertainty is #" ml%
 
 So uncertainty is # $%$& ,c
.alue temperature can be *%*& ,c or *%'&,c
  Uncertainty in digital instruments:
 $%ample 1 :
 / measurement of a sample is '*%* g
so the value can be '*%'or '*%+g g 
 
 )uestion
 / sample is measured on an analogue weigh scale and a digital
weigh scale the value is *&%& g 0 what will be the uncertainty and the
expected values 1
 /nalogue expected values between *&%&& and *&%+& g 
 Digital expected values between *&%( and *&%+ g 
3he analogue weigh scale has a lower uncertainty 44
 ,ther sources o" uncertainty:
 -oltage electrochemical cell
 1 andom errors 'appro%imating a reading(
 / eada0ility o" measurement instrument
 / $""ects o" changing surrounding
 / nsu""icient data
 2 systematic errors 'poor design or procedure human error(
 / eading +rong meniscus height #olume liquid in cylinder
 / ,#ershooting #olume in titration
systematic errors cannot 0e reduced 0y repeated measurement
 
55
55
55
55
55
Measurement o" !ata *ccurate Precise
Value volume liquid = 67.5 ml
55.3ml, 69.4 ml, 56.8 ml, 63.7 ml, 66.5 ml
Mass of a sample of NaOH = 7.67 g
8.32 g, 8.34 g, 8.35 g, 8.3 g, 8.33g, 8.36 g
Value !empe"a!u"e of #a!e" = 24.5 $%
24.8 $%, 23.8 $%, 25.$%, 24.& $%, 24.9 $%, 24. $%
'H value of a liquid = 7.83
7.82, 7.85, 7.84, 7.8, 7.83, 7.82, 7.84
6o da!a fa"
6o da!a fa"
value
o!)e" 
 
The accuracy o" a measurement is gi#en 0y the percent error
8 $rror 9 Measured -alue / *ccepted -alue
*ccepted -alue
$%ample
*n o0ect is ;no+n to +eigh 2<.= grams. 7ou +eight the o0ect
as 2>.2 grams. ?hat is the accuracy o" your measurement@
8 $rror 9
2<.= g 9 B. 8
% 1==
% 1==
  Percentage uncertainties and errors
the sum o" the a0solute uncertainties
 $%ample
 )nitial reading "&%$& cm* # $%$& cm* 5"&%$$-"&%"$ cm* 6
7inal reading *8%'$ cm* # $%$& cm* 5*8%"&-*8%'& cm*6
 . max  9 *8%'& : "&%$$ 9 ''%'& cm* 
. min 9 *8%"& : "&%"$ 9 ''%$& cm* 
3herefore .olume 9 ''%"&#$%"cm*
 )nitial reading "'%* cm* # $%& cm*
7inal reading *?%' cm* # $%& cm*
. min 9 *%8 : "'% 9 '&%? cm* 
3herefore .olume 9 '(%?#"cm*
 ;rror < 9 "='(%? > "$$< 9 *%8'<
Dind the a0solute error and error 8 o" the reading
 *ns+er
?hen Multiplying or di#iding measurements the total
uncertainty 8 is the sum indi#idual 8 uncertainties
The a0solute uncertainty can then 0e calculated "rom
uncertainty 8
t+o +ays
 
 $%ample
< uncertainty Mass 9 5$%&='+%$6 > "$$ < 9 '<
< uncertainty .olume 9 5$%"='%$6 > "$$ < 9 &<
 Max value D 9 '+%&="%? 9 "'%?
 Min .alue D 9 '*%&='%" 9 ""%"?
 /bsolute uncertainty 9 "'%?- "'%$$ 9 $%? gcm-*
< D 9 5$%?="'6 "$$< 9 8%+ < 5value in ' s%f 6 answer! 8<
Method 1
< uncertainty D 9 '< @ & < 9 8 <
 Method 2
  AD=D 9 AM=M @ A.=.
 AD="' 9 $%&='+%$ @ $%"='%$ AD 9 $%&
 6o+ you
7ind the value of the volume0 uncertainty and < uncertainty from
 following measurements ! 9 *%+$ #$%$& m0 B 9 "%8$ # $%$&m0 9
$%8& # $%$&m
 8 uncertainty
  9 *%+$ #$%$& m
 [2]#a$ a&ue V =4.'3 #in Va&ue = 3.59 :
a*&ute uncertainty  = 0.49+ % ,ncertaintyV =
0.49/4.34 = 11.3% 11%
 -V = 0.111 a*&ute % uncertinty V = 11%
. 9 +%*+ # $%+? ercentage Encertainty 9 ""<
 11.3 Graphical techniques
  Plotting graphs  - Five the graph a title - abel the axis with both quantities and units
- Ese available space as effectively as possible
5minimum &$< of graph paper6
- use linear scale 5no uneven Gumps6
 - lot all points correct0 the line of best fit should be smoothly
  5not from point to point6
$%ample graphs
7inding gradient and intercept 
Dor a straight line y9 M% F C % is the independent #aria0le
m is the gradient %
To "ind gradient use triangle method 'has to co#er min <= 8 o" graph(
n this e%ample % 9 <=< 9 1= Hcmin/1
 C 9 intercept is &$ ,c
 
Unit > ;inetics 'rate o" reaction etcI(