maths standard
TRANSCRIPT
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Sergej Sedunov
Maths Standard
Mathematical Exploration of the amount of the goals scored in therst and second halves.
Exam Session: May 2015School Name: Impington International th!orm
"ourse: Maths Standard
Name: Sergejs Sedunovs
"andidate Num#er:
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$a#le o% "ontentsIntroduction:&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& '
Method:&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& '
"alculations:&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&5
Mean:&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 5
Standard (eviation:&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&11
"onclusion:&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 2'
)imitations:&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 25
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Introduction:*hen I +as trying to ,nd a research topic %or my investigation I thought o%choosing an area to explore that interests me the most& Since I-m a #ig %an o%
%oot#all I decided to +or. around this area and thought o% an idea that I
heard previously +hile +atching %oot#all& $his idea +as to do +ith
commentators stating the %act that it is very common that most o% the goals
are scored in the second hal% rather than in the ,rst one& *hile I also loo.ed
at the other ideas/ this topic +as the one that stood out to me and this +as
due to the %act that there +as no similar investigations in that area/ even.no+ there +ere other %oot#all areas that +ere mathematically explored& In
order to choose the right %oot#all tournament %or carrying out this
investigation I thought o% pro#a#ly the #iggest European tournament .no+n
as "hampions )eague&
$he +ay I decided to plan my investigation is to process the ra+ data %rom
the ue%a&com +e#site +hich provides the history o% the previous "hampions
)eague seasons& s there +as no data that +as processed already %or my
investigation&
$he main aim o% my investigation is to see +hether there +ill #e more goals
scored in the ,rst hal% or in the second hal% and %rom that dra+ the
conclusions regarding +hat I have heard in the past %rom the commentators
+hile +atching %oot#all&
Method:In my investigation I collected secondary data see ppendix 1 %rom 3E!
# it 1 M d t i l d d th h l l ti 2 % t
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+hat +as more in9uential in terms o% the overall mean/ group stages or play6
o8s&
Calculations:Mean:
$he mean is the average o% the num#ers: a calculated central value o% a
set o% num#ers&In my investigation I used mean in order to see ho+ did the
mean num#er o% goals scored in the ,rst and second hal% vary in the group
stages and play6o8s& So later I +ould #e a#le to see ho+ the group stages did
and play6o8s a8ected the overall mean&
Formulae:
X ; XN
Season 20!"20#:
$roup stages % st
half
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$roup stages % 2ndhalf
X ;165
96 ; 1&=2
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X ;37
29 ; 1&2>
&la'(o)s % 2ndhalf
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X ;151
125 ; 1&21
*verall +&la' o)s , group stages- 2nd half
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Season 202"20#:
$roup stages % sthalf
X ;133
96 ; 1&
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*verall +&la'(o)s , group stages- % 2ndhalf
Sxx B 1&2
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Conclusion:In my conclusion I +ould say that my main hypothesis +hich +as that the
amount o% goals scored in the second hal% +ould #e more than in a ,rst hal%+as approved #y the data that I collected and analysed& In order to support
my conclusions I presented the data o% Mean and Standard (eviation in
separate ta#les $a#le 1 and $a#le 2 %or t+o season 2014201' and
20124201& Cy loo.ing at the overall mean +hich includes #oth group stages
and play6o8s o% #oth seasons/ it is possi#le to see that in #oth seasons
2014201'/ 20124201 the overall means o% second halves 1&> and 1&
+as higher than the mean o% ,rst halves 1&21 and 1&1& $he #iggestin9uence on the overall mean o% the second halves in the season 2014201'
+as %ound to #e in the group stages/ ho+ever in the season 20124201 the
overall mean +as more in9uenced #y play6o8s& It is +orth+hile mentioning
that the amount o% games in play6o8s 2
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Standard
eviation
1&1' 1&1> 0&
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ppendices
2014201' 3") Season
$roup stages
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2014201' 3")5Season
&la'(o)s
5 3E! "hampions )eague
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20124201 3") Season
$roup stages
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20124201 3") Season
&la'(o)s