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Averages
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Contents
Introduction 3
Slide Number
Key Words 5
Averages 7
Range 23
34rou!ed "ata
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Averages
#$ere are t$ree di%%erent ty!es o% averages
&ode
most common
&edian
middle value &ean
sum o% itemsnumber o% items
Range is $o' %ar %rom t$e smallest to t$e largest(
Range ) *argest + smallest
,b-ective . #o /no' t$e t$ree di%%erent averages(
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&I
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N
S
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S#
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& 0 A N
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R A N 0
0asy Way #o Remember #$e #$ree Averages and #$e Range
& , " 0
I 1 I " 0
,b-ective . #o /no' t$e t$ree di%%erent averages(
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KeyWords
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Key 'ords
R a ' d a
t a" a t a b e % o r e i t i s a n a l y
s e d (
r o u ! e
d d a t a
" a t a ' $ i c $ i s c o m b i n e d i n a n i n t e r v a l (
A v e r
a g e & e a n 2 & e d i a n o r & o d e (
R a n g
e # $ e s ! r e a d o % d a t a (
,b-ective . #o understand t$e terms used(
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&ean
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Averages + &ean
All t$e data is added u! and t$e total divided by t$e number o%items( #$is is called t$e mean and is euivalent to s$aring outall t$e data evenly( 0very value a%%ects t$e mean(
0am!le
ere are t$e 'eig$ts o% 6 s!rinters in /g(ind t$e mean 'eig$t(
88 9 :; 9 7: 9 :4 9 86 9 :< ) 528 /g#$e mean is 528=6 ) 88/g
,b-ective . #o /no' $o' to use t$e mean as an average(
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>uestions on &ean
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>uestions on &ean
3( ere are t$e 'eig$ts o% 5 %emale s!rinters in /g(
75 8< 64 58 62
ind t$eir mean 'eig$t(
4( ere are t$e $eig$ts o% 5 %emale s!rinters in cm(
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>uestions on &ean
5( ere are t$e 'eig$ts o% 6 male 'restlers in /g(
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&edian
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Averages + &edian
#$e number o% medals 'on by a!an are .
2: 25 ; 32
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>uestions on &edian
2( ind t$e median o% t$ese s$oe siGes .
: 5 3 8 4 3 6 7
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>uestions on &edian
5( ind t$e median o% t$ese s$oe siGes .
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&ode
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Averages + &ode
#$e mode number o% mar/s scored in a test(
#$e number o% items '$ic$ occurs most %reuently is called
t$e mode( #$is is t$e most !o!ular value(
,b-ective . #o /no' $o' to use t$e mode as an average(
o$n < #anya 8 Hen 5Sara$ 6 aid 4 Kara 4
&ic$ael 2 atima
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>uestions on &ode
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>uestions on &ode
2( A bar c$art s$o's t$e scores in a Science #est .
ind t$e modal Science score(
Bar Chart To Show Science Scores
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8 9 10
Marks Scored
N o . o
f P u p i l s
A mar/ o% 6 $ad t$e $ig$est bar so t$e modal Sciencescore is 6(
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>uestions on &ode
3( A !ie c$art s$o's t$e %avourite #1 C$annels.
ind t$e modal #1 c$annel(
A Pie Chart To Show
Favourite TV Channel
45
20
15
20
SKY
ITV
BBC
OTH!
#$e biggest sector o% t$e !ie c$art is %or S/y so t$emodal #1 c$annel is SKJ(
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>uestions on &ode
4( A !ie c$art s$o's t$e %avourite %ood.
ind t$e modal %ood grou!(
Favourite Food
75
2518
55
22
"#o"o$at%&r'(t
)%*%ta+$%s
sw%%ts
ot#%r
#$e biggest sector o% t$e !ie c$art is %or c$ocolate so t$emodal %ood grou! is c$ocolate(
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>uestions on &ode
5( 8A did a &at$s #est on Algebra t$e %ollo'ing are t$eir scoresin !ercentages.
o$n 8< #anya 48 Hen 5:Sara$ 76 aid 54 Kara 48&ic$ael 52 atima :; ames 77
Amanda 53 &ary 7: "aniel 56Craig 66 1ictoria 55 Katie 47Samant$a 37 Ansar 45 anna$ 45C$ris 34 Amy 63 Nasim 52Abad 52 Nic/y 62 oanne 2:
unaid 7<
W$at is t$e modal !ercentage
#$ere are t$ree scores o% 52 and so 52 is t$e modal !ercentage(
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Range
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Range
Range
#$e range is a measure o% t$e s!read o% data(
*argest value + smallest value
#$e %ollo'ing are scores in a renc$ #est .
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KeyWords
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Key Words
Ascending
"escending
Numbers '$ic$ are increasing in value
Numbers '$ic$ are decreasing in value
0am!les o% Ascending and "escending
3 4
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>uestions
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>uestions
o$n < #anya 8 Hen 5Sara$ 6 aid 4 Kara 4&ic$ael 2 atima
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>uestions
5( ind t$e range o% t$ese s$oe siGes .
: 5 3 8 4 3 6 7
6( ind t$e range o% t$ese t$ro's on a dice .
6 3 2 5 4 4 3 4
7( ind t$e range o% t$ese scores .
32 24 56
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0!lanation
0ac$ average $as its !ur!ose and sometimes one is more!re%erable(
#$e median is very easy to %ind and $as an advantage in being$ardly a%%ected by etreme values + big or small(
#$e mean ta/es into account all t$e values including etremevalues(
#$e mode alt$oug$ most !o!ular ta/es into account all t$edata( I% t$ere are any etreme values t$en t$ese a%%ect t$emean(
#$e mode is easy to calculate and it eliminates some o% t$ee%%ects o% etreme values( It $as its disadvantageses!ecially '$en t$ere are t'o modes( #$is is '$y t$is averageis not 'idely used(
,b-ective . #o /no' '$en to use t$e t$ree averages(
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>uestions
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>uestions
3( #$e %ollo'ing are t$e amounts 5 !eo!le made on t$estoc/ mar/et .
&r ,range . 225;; &r W$ite .
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>uestions
,n t$e tele!$one to a buyer $e describes t$e co's as $avingan average 'eig$t o% around
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rou!ed"ata
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rou!ed "ata
#$e results o% 5< !u!ils in a "ata andling test are given in t$e%reuency table(ind t$e mean median and mode(
,ark 30-39 40-49 50-59 60-69
&r%.'%/" 7 14 21 9
#o 'or/ out t$e mean 'e %ind t$e mid !oint o% eac$ interval(Mean ) ?34(5 7@ 9 ?44(5
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>uestions
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>uestions
2( #$e number o% C$ristmas cards received by 26 !u!ils'ere as %ollo's .
number o% cards %reuency
; to 2
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