statistics averages

8/17/2019 Statistics Averages

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© Boardworks Ltd 2001

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

"

*

0

& 0 " I A N

C

&&,

N

S

&A**

S#

*

R0S#

& 0 A N

""

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(


9/37© Boardworks Ltd 2001

>uestions on &ean



>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(



>uestions on &ean

5( ere are t$e 'eig$ts o% 6 male 'restlers in /g(



&edian



Averages + &edian

#$e number o% medals 'on by a!an are .

2: 25 ; 32



>uestions on &edian

2( ind t$e median o% t$ese s$oe siGes .

: 5 3 8 4 3 6 7



>uestions on &edian

5( ind t$e median o% t$ese s$oe siGes .



&ode



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



>uestions on &ode



>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(



>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(



>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(



>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(



Range



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 .



KeyWords



Key Words

Ascending

"escending

Numbers '$ic$ are increasing in value

Numbers '$ic$ are decreasing in value

0am!les o% Ascending and "escending

3 4



>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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