Group 22 Assignment 7 Draft
Transcript of Group 22 Assignment 7 Draft
-
8/18/2019 Group 22 Assignment 7 Draft
1/24
1ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
Assignment 7: Statistics
Group 22 Members:
Benedicto Munthali
Roelof Jacobs
Kevin olmin!
"holl# e$i
John Ro%burgh &"'(
)ord *ount)ords +"ables ,igures -./
"otal + 6446
Abstract
"his report loo!s at four different case studies to demonstrate different
statistical anal#sis functions0 "he follo1ing statistical concepts are
investigated0 ormal distribution3 stastistical difference from a mean3
significance of difference bet1een a set of t1o results3 reproducibilit#3
repeatabilit#3 and correlation bet1een dependent results0 4t also e%plores
errors and measurement uncertainties0 Results are related to 1hat could be
e%pected from concrete0
Page 1 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
2/24
2ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
Group Assignment 7 Statistics
-0 "he concrete for the central core of a high+rise building is re5uired to have a
modulus of elasticit#3 63 of / G8A for deflection control0 "he concrete supplier
has carried out a series of tests on successive batches of a potential concrete andobtained the follo1ing values for 6:
-0/3 /0/3 903 90;3 2073 -03 -0;3 -03 /03 9iscuss an# action that #ou could ta!e if #ou 1ere the technical manager 1ith
responsibilit# for these t1o plants0
"able -
90 @ou have been as!ed to evaluate the performance of t1o laboratories in
measuring the properties of 8ortland cement0 "o assist #ou in this3 #ou have
as!ed each laborator# to carr# out repeat tests &to BS 6 -;+-( on cement
samples ta!en from a single batch of cement0 "he values of initial set and 2< da#
compressive strength obtained b# each laborator# are given in table 20
)hat conclusions can #ou dra1 from these results=
Page 2 of 24
2< da# concrete strengths&M8a(
batch no plant - plant 2
- 0/ -0/
2 90. -0/
9 ./0. .0/
0. ;0.
. .0. 0/
; 20/ ;0.
7 .0/ 0.
< 0/
;0.
-
8/18/2019 Group 22 Assignment 7 Draft
3/24
ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
"able 2
Page 3 of 24
initial set &mins( 2< da# strength &M8a(
'aborator#- 'aborator# 2 'aborator# - 'aborator# 2
-9/ -2 70
-
8/18/2019 Group 22 Assignment 7 Draft
4/24
!ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
0 "he results in "able 9 have been obtained on tests on a set of concretes made
1ith the same aggregates and the same 8ortland cement0
a0 )hat conclusions can #ou ma!e about the use of strength tests at 9 da#s
for predicting 2< da# strength for 5ualit# control purposes=
b0 *ompare and contrast the relationships bet1eeni0 the mi% proportions and the measured properties
ii0 the ultrasonic pulse velocit# and compressive strength
1ith e%pected or t#pical relationships0
"able 9
mi% proportions &!gm9( properties
cementfree
1ater
aggregate 2/&SS>(
aggregate /&SS>(
slump&mm(
cube strength&M8a(
ultrasonic pulsevelocit# at 2<
da#s
&!msec(
9
da#s
2<
da#s.// -/ ---/ ./ 7. 9-0. .;0. 0
-
8/18/2019 Group 22 Assignment 7 Draft
5/24
"ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
++++++++++++++++++++++++++++++++++++++
• 4n #our ans1ers #ou should clearl# set out #our reasoning3 calculations and
assumptions etc0 throughout0
• Overall maximum length 7000 words &e%cluding report title page3 contents3
reference list and appendices3 but including 1ords in tables( 1ith each diagram3figure etc0 1ithin the main te%t to count as -./ 1ords0
• Ke# diagrams3 figures etc0 should not be relegated to appendices0
• umber of 1ords or 1ord e5uivalents should be declared on the title page0
D"6:
"his assignment consists of a progressive set of 5uestions3 and therefore 1e
suggest that all members of the group focus on each 5uestion in turn3 and agree on
the ans1ers before proceeding to the ne%t 5uestion0
Page 5 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
6/24
#ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
Table of ontents! "age
#$ Statistical anal%sis on results obtained from testing concrete
samples for modulus of elasticit%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$6
#$# &ntroduction$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$6
#$' x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$6
#$( x $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$7
#$($# x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$)
#$($#$# x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$)
#$($#$' x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$*
#$($#$( x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#0
#$4 x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#'
#$4$# x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#'
#$4$' x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#+
#$4$( x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#7
Page 6 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
7/24
7ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
Table of ontents cont! "age
'xxxxx$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ #)
'$# &ntroduction$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#)
'$' xx$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#)
'$'$# xx$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#)
'$'$#$# x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#)
'$'$#$' x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#*
'$'$#$( x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'0
'$'$' x $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'#
'$( x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'6
'$($# x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'6
'$($' x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'7
'$($( x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'7
'$4 onclusion$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'*
,eferences!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(0
Page 7 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
8/24
$ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
#$ Statistical anal%sis on results obtained from testing concrete
samples for modulus of elasticit%$
#$# &ntroduction
"he modulus of elasticit# re5uired for a high+rise building is / G8a0 "his 6 value is
re5uired for deflection control0 Statistical evaluation should be done to prove both
normal distribution of the data
'$ Anal%sis on reproducibilit% between two concrete plants$
'$# &ntroduction
90 Repeatabilit# and Reproducibilit# tests on setting times and 2< da# strengths of a
single batch of cement using t1o different laboratories0
Batch No.
28 Days ConcreteStrengths(Mpa)
Pant 1 Pant 2
1 !% !1
2 %&" !1
3 "0&" !"
4 !!&" !#&"
5 "!&" !!6 !2 !#&"
7 "! !!
8 !%
! !#&"
Me"#an !% !!&"
Co$nt 7 %
SD "&$" 2#
S%aest %&" !1
&argest "!&" !%
"' 1" $
Pant 1D#str#$t#on
C$r*e
Pant 2D#str#$t#on
C$r*e
Pant1 B#n
+re,$ency
Pant1 B#n
+re,$ency
%&" 1 !1 2!2 1 !1&" 0
Page 8 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
9/24
%ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
!!&" 1 !2 0
!7 0 !2&" 0
!%&" 0 ! 0
"2 0 !&" 0
"!&" 1 !! 2
!"&" 0
!# 0
!#&"
!7 0
!7&" 0
!$&" 0
!%& 1
-ae 2.
Variable 1 Variable 2
Mea' !$ !"
ara'*e ! 7
Ob+ervao'+ 7 %-./oe+e Mea'34ere'*e 0
f $ Sa 1&20%2#0
Page ! of 24
-
8/18/2019 Group 22 Assignment 7 Draft
10/24
10ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
P(T56) o'ea8 0&10"!2
Cr*a8 o'ea8 1&$"%"!$
P(T56) 9oa8 0&2#10$"
Cr*a8 9oa8 2&0#00!
' $-a.$' omparison population of means
HO 1 / 2 Te '88 ./oe++ e. are e +ame +re'
H1 1 0 2 Te a8er'ave ./oe++ e. are4ere'
Pant 1 Pant 2
SE 6 n SE 6 n
6 "&$";e'*e 'erva8 a "=8eve8
Pant 1 t *a$e / 7 1 Pant 2 t
*a$e / ! 1
/ 6 / 8
there'ore t*a$e 'or5 o' 'ree"o%
there'oret*a$e 'or
5 o' 'ree"o%(26) (28)
/ 5.14 / 4.46
t *a$e 9 S: / 5.14 9 2.21t *a$e 9 S:
/ 4.46 .887
there'ore;11.36 'or pant1 /
;3.!6'orpant 2
erefore fo88o9+ a e e+mae of e /o/8ao' mea' from e +am/8e mea'?
Page 1 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
11/24
11ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
@or P8a' 1 + !$ 11&#
a + ra'ge+ from #! o"%&#
@or P8a' 2 + !" &%#
a + ra'ge+ from !1&0! o!$&%#
The ranges for Plant 1 and Plant 2 do not overlap at the 95% condence level and therefore
conclude that population means are dierenteg! there is a signicant dierence in the concr
"o #e re$ect the ull H&pothesis!
20b( As per anal#sis done above 3the standard deviation and population mean for 8lant - is too hi *oncrete 5ualit# 1ill be compromised and this can increase production costs3 because target st
b# characteristic strength plus standard deviation times ! factor0
Batch records must be retrieved and evaluated for compliance0
Scales and plant e5uipment 1ill to be calibrated
Ra1 materials at the plant must be sampled and tested0
"rial mi%es must done to assess 1ater demand0
Batch 8lant personnel must be re+trained0
"ruc! mi%er inspections must the done
*ompliance to sampling 3cube ma!ing and crushing procedures 1ill have to be assessed
'aborator# staff 1ill have to be retrained
($0&ntroduction
( Assumptions
"he follo1ing are the assumptions for this 5uestionE
• "he cement sample ta!en from the batch follo1s a normal distribution curve
• "he cement sample provided to both laboratories has the same mean and
standard deviations
• "he e5uipment in both laboratories is of the same 5ualit# and same 4SD
certification
Page 11 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
12/24
12ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
($# Statistical anal%sis of the data
*onsidering that in both laboratories3 -/ observations 1ere made on initial setting
time and -2 observations 1ere made on 2< da# strength3 the data 1ill be anal#$ed
b# "+test and ,+test0 Belo1 is the data presentation0
Table #! Observation for /ab # /ab '
4nitial set &mins( 2< da# strength &Mpa(
Sample
F 'aborator# - 'aborator# 2 'aborator# -
'aborator#
2
- -9/ -2 70
-
8/18/2019 Group 22 Assignment 7 Draft
13/24
1ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
1igure #! omparison of &nitial set for /ab # /ab '
According to 6 -;+-3 the initial set for the cement had to greater than ;/ minutes
&Ref(3 both laboratories have sho1n that the cement is clearl# above its initial set
time0
*onsidering for "+test and ,+testE
2ull h%pothesis: "he means from the laboratories are e5ual &"+test(
Alternative h%pothesis: "he means from the laboratories are not the e5ual
2ull h%pothesis! "he variances from both laboratories are e5ual &,+test(
Alternative h%pothesis! "he variances from both laboratories are not e5ual
4n both cases H /0/. for .I confidence level
"esting the data as paired "+test3 the follo1ing results 1ere obtainedE
Table '! t3Test "aired Two Samples of eans
t+"est: 8aired "1o Sample for Means
Lab 1 Lab 2
Mean -9-0 -2902ariance 2/0/ -;0-777777<
Page 13 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
14/24
1!ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
Dbservations -/ -/
8earson *orrelation /0/./..ifference /
df
t Stat 02--97/-
8&"Ht( one+tail /0///
-
8/18/2019 Group 22 Assignment 7 Draft
15/24
1"ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
1igure '! omparison of the two laboratories ') da% strengths
,ollo1ing the same null and alternative h#potheses mentioned above3 the paired t+
test gives the follo1ing results are obtainedE
Table (! t3Test paired two sample for ') da% strength means
t+"est: 8aired "1o Sample for Means
Lab 1 Lab 2
Mean .0-.
-
8/18/2019 Group 22 Assignment 7 Draft
16/24
1#ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
Since 8 &"Ht( is greater than /0/. &(3 1e re?ect the null h#pothesis and the means
are not e5ual hence significantl# different0
"esting the variance using the ,+test 1e find the follo1ingE
,or initial setE
Table 4! 13test Two 3 Sample &nitial Set 5ariance
,+"est "1o+Sample for ariances
Lab 1 Lab 2
Mean -9-0 -2902
ariance 2/0/ -;0-777777<
Dbservations -/ -/
df
, -029/-/
-
8/18/2019 Group 22 Assignment 7 Draft
17/24
17ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
,or the initial set3 1e re?ect the null h#pothesis3 the variances are significantl#
different and for the 2< da# strength3 1e accept the null h#pothesis3 the variances
are significantl# the same &e5ual(0
($' iscussion and onclusion
"he table belo1 sho1s a summar# of the situation
Table 6! Summar% of t3test and 13test anal%sis
"+test out come ,+test out come
*omparison of lab - and
lab 2 on initial set
Significantl# the same
means
Significantl# different
variances
*omparison of lab - and
lab 2 on 2< da# strength
Significantl# different
means
Significantl# the same
variance
Going bac! to figures - and 2 1e see that for the initial set &fig -(3 both laboratories
and uncontrollable variances 1hich agrees 1ith the ,+test findings0 "his might have
been because both laboratories had ine%perienced technicians carr#ing out the test0
,rom fig 23 2< da# strength3 1e see that laborator# 2 had a better controlled series of
results than laborator# -0 "he variance is 1ell controlled and consistenc# is
maintained in lab 20 "his is 1h#E the means of the t1o laboratories differ0 4t could be
interpreted that lab 2 had competent personnel to carr# out this test or had a better
5ualit# control monitoring s#stem as compared to lab -0
Based on the above evidence3 both laboratories have poor monitoring s#stems
orand less competent personnel to carr# out initial set tests and laborator# 2 has a
better monitoring s#stem orand competent personnel to carr# out 2< da# strength0
Luestion 9
b("he standard deviation for 8lant - is too high3compared to 8lant 20
"herefore the follo1ing 1ill have to be done0
• Batch records 1ill have to be evaluated for compliance0
• Scales and plant e5uipment 1ill have to be calibrated0
• Ra1 materials 1ill have to be sampled and tested0
• "rial mi%es 1ill be done to assess 1ater demand
•
8lant personnel 1ill have to be re+trained• "ruc! mi%er inspection 1ill have to be conducted0
Page 17 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
18/24
1$ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
• *ompliance to sampling 3cube ma!ing and crushing procedures 1ill have to
be assessed0
• 'aborator# staff 1ill have to be re+trained0
4. Concrete %a"e
-
8/18/2019 Group 22 Assignment 7 Draft
19/24
1%ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
@gre Jo9 9aer *eme' rao
*eme'
free9aer B;C
*be +re'g(MPa) +8m/ Sre'g
Ga'
a.+
2$a.+ (mm)
10 17" 0&"# 1&$ 7&" !0 7=
10 17" 0&"# 2&1 7&" "0 #2=
10 1%" 0 1!&% 0&$ $" !$=
2"" 170 0 1%&$ 0&1 0 ##=
22" 1#" 0&7 7&2 1$&2 0 !0=
2$" 210 0&7! 10&1 17&" 1$0 "$= S3 o'
+re'gga'
2"" 1%0 0&7" 1"&" 22&" #0 #%=
22" 170 0&7# %&2 1$&7 20 !%=Averag
e "= 11&$% Tab8e -g 9aer *eme' rao
@gre -g 9aer *eme' rao
Conc$s#ons
Page 1! of 24
-
8/18/2019 Group 22 Assignment 7 Draft
20/24
20ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
Tere + a eafe'e *orre8ao' be9ee' e ear8. age +re'g a' e
2$a. +re'g of *o'*ree& -o9ever e a. re+8 a+ a bg varab8.
e o fa*or+ 8De e +8m/& Te +'g a 7 a. re+8+ a+ a /re*o' +
more 9e8. +e ' '+r.&
Te +e of +a+*a8 /rogram+ a 9orD 4ere' e+g' +re'g ba*D oo'e e+g' +re'g 8De a 2"MPa + a8+o +e& T+ a88o9+ e Ka8.
/er+o' o more ea+8. +ee f ere + a /rob8em 9 e *o'*ree&
4..#. M#9 proport#ons an" %eas$re" propert#es
4..##.>trason#c p$se *eoc#ty (>P?) an" co%press#*e strength.
m /ro/oro'+ (Dg;m) /ro/ere+
*eme'
free9aer 9;*
*be +re'g(MPa) 8ra+o'* /8+e ve8o*. a 2$ a.+
a.+
2$a.+ (Dm;+e*)
"!" 20" 0&$ 22&$ !7&% !&7
"00 1%0 0&$ 1&" "#&" !&$
"!" 22" 0&!1 2&" !%&" !&72
%0 1%" 0&"0 1&2 "&2 !"
%0 200 0&"1 20&! !0&2 !"
%0 20" 0&" 2%&1 !! !&7"
10 17" 0&"# 1&$ 7&" !
10 17" 0&"# 2&1 7&" !&72
10 1%" 0 1!&% 0&$ !&""
2"" 170 0 1%&$ 0&1 !&!"
22" 1#" 0&7 7&2 1$&2 !&"
2$" 210 0&7! 10&1 17&" !&2
2"" 1%0 0&7" 1"&" 22&" !&"2
22" 170 0&7# %&2 1$&7 !&$ Tab8e UP a 2$3a. +re'g
Page 2 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
21/24
21ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
@gre 2$3a. UP aga'+ B;C rao
@gre 2$3a. Cbe +re'g aga'+ B;C rao
Tere + obvo+8. a 'ee for a re8ab8e 'o'e+r*ve e+ meo o
*om/8eme' or re/8a*e e e+'g e+r*ve mea'+ of verf.'g e
+re'g of *o'*ree ' Ke+o' o' +e& Te UP + o9ever 'o *rre'8.
+e a+ e /rmar. meo of e+'g, b +e a+ a +//8eme'ar.
'*aor of e Ka8. of *o'*ree ' +r*re+& T+ + be*a+e e
re8ao'+/ be9ee' *om/re++ve +re'g of *o'*ree a' UP + 'o
+m/8e& (LL Poo', 1%%)
Page 21 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
22/24
22ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
Te aggregae ./e a' e amo of aggregae a + ++/e'e ' e
*o'*ree a+ a bg e4e* o' e re+8+ a are a*eave 9 e UP
meo+& (& J', 200)
Be' av'g a 8ooD a e 2$a. UP a' e 2$a. +re'g *om/are o
e 9;* o'e *a' +ee a +'* re8ao'+/&
Conc$s#on
Tere + a '*ao' a e UP *a' be +e for e /re*o' of e
2$a. +re'g o' +e& Tere + o9ever a fe9 +or fa88'g+:
a& Te UP 988 ave o be *a8brae o' a +e*o' of D'o9' *o'*ree of e +ame maera8 a' *om/o+o'&
b& Te re8ao'+/ be9ee' *r'g a' e em/erare a 9* a//e'+ a8+o /8a.+ a /ar ' e varab8.& (& S', 200")
*& Te 8o*ao' a' +rbo' of .or re'for*e +ee8 ' e +r*re&
& Com/a*o' of e *o'*ree member
F. aD'g 'o *o'+erao' a88 e 4ere' /arameer+ I 9o8 +e e
UP +.+em+ o'8. a+ a' '*ao' a' a ver>*ao' +.+em or o e'f.
a /o++b8e /rob8ema* area ' .or +r*re&
a. B##ographyLL Poo', T& B& (1%%)& 3eve8o/eme' of +a+*a8 Ka8. a++ra'*e *rero' for
*o'*ree +'g UP meo+& '() *aterials +ournal , "#$"7&
Sear, J& (200)& a8. *o'ro8& I' F& S& & Ne9ma', 'dvanced (oncrete
Technolog& (//& %;1%;2!)& Ofor: Fer9or-ema''&
& J', C& J& (200)& Pre*o' of UP ' *o'*ree& '() *aterials +urnal , 212$&
& S', T& & (200")& Tem/erare e4e*+ o' +re'g eva8ao' of *eme' ba*e
9 8ra+o'* 9ave reQe*o' e*'ge& '() *aterials +ournal , 27227$&
Page 22 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
23/24
2ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
+ onclusion$
Page 23 of 24
-
8/18/2019 Group 22 Assignment 7 Draft
24/24
2!ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22
,eferences!
2 2