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STATISTICSBy: Johanne H. Rivas
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STATISTICS
Statistics is a mathematical sciencethat deals with the methods in the
collection, presentation, analysis andinterpretation, as well as drawingconclsions!generali"ations o# data.
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$S%& '( STATISTICS It can give precise prescription o# data.
It can predict )ehavior o# individals.
It can )e sed to test hypothesis.
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STATISTICA* +%TH'&S&escriptive statistics
Correlational statistics
In#erential statistics
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&%SCRITI-% STATISTICS&escriptive statistics descri)e the main #eatreso# a collection o# data antitatively. &escriptive
statistics are distingished #rom in#erentialstatistics /or indctive statistics0, in thatdescriptive statistics aim to smmari"e a dataset, rather than se the data to learn a)ot thepoplation that the data are thoght to
represent. This generally means that descriptivestatistics, nli1e in#erential statistics, are notdeveloped on the )asis o# pro)a)ility theory.
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C'RR%*ATI'2A*STATISTICS
In statistics, dependence re#ers to anystatistical relationship )etween two
random varia)les or two sets o# data.Correlation re#ers to any o# a )road classo# statistical relationships involvingdependence.
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I2(%R%2TIA* STATISTICS
In statistics, statistical in#erence is theprocess o# drawing conclsions #rom data
that are s)3ect to random variation. +ores)stantially, the terms statisticalin#erence, statistical indction andin#erential statistics are sed to descri)e
systems o# procedres that can )e sed todraw conclsions #rom datasets arising#rom systems a4ected )y randomvariation.
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HIST'R5 '( STATISTICSSome scholars pinpoint the origin o# statistics to6778, with the p)lication o# 2atral and olitical
')servations pon the Bills o# +ortality )y John9rant. %arly applications o# statistical thin1ingrevolved arond the needs o# states to )ase policyon demographic and economic data, hence its statetymology. The scope o# the discipline o# statistics)roadened in the early 6;th centry to inclde thecollection and analysis o# data in general. Today,statistics is widely employed in government,)siness, and the natral and social sciences.
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Its mathematical #ondations were laid in the
6
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'$*ATI'2 A2& SA+*%
A poplationis a set o# people or o)3ects yoare interested in #or a particlar stdy. It can )e a=niteor an in=nite poplation.
A sample is a collection o# elements ta1en #rompoplation. It can )e a )iasedor an n)iasedsample.
A randomsampleis a selected sample sch
that every mem)er o# a poplation has an ealchance o# )eing chosen.
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SA+*I29 T%CH2I@$%S
Samplingis selectinga parto# a poplation torepresentthe poplation.
Types:
pro)a)ility sampling
nonpro)a)ility sampling
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R'BABI*IT5 SA+*I29
In pro)a)ility sampling, each mem)er o# apoplation has a 1nown pro)a)ility o# )eingselected.
Types:
random sampling
strati=ed random sampling
clster sampling
systematic sampling
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2'2R'BABI*IT5 SA+*I29
In nonpro)a)ility sampling, samples are notchosen at random.
Types:
ota sampling
prposive sampling
accidental sampling
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ARA+%T%RS A2& STATISTICS
arameter a nm)er that represents or descri)esa poplation.
Statistic a nm)er that represents or descri)es asample.
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-ARIAB*%S A2& &ATA
-aria)le the characteristic or property o# a nit o#a poplation.
&ata a set o# o)served characteristic a)ot apoplation.
&ata set a collection o# data.
&ata point a single o)servation.
Raw data data that have not )een arranged oranaly"ed.
The data a)ot a poplation may )e antitativeor alitative.
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-ARIAB*%S I2 STATISTICS According to #nctional relationship:
dependent
independent According to continity o# vales:
discrete
continos
According to levels o# measrement:
nominal
ordinal
interval
ratio
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2'+I2A* SCA*%
In the nominal scale o# measrement,o)servations are groped into classes accordingto some attri)tes or properties.
%?ample:racial origin
eye color
Category
real nominal /real nominal dichotomos0arti=cial nominal
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'R&I2A* SCA*%
hen di4erent degrees o# a certain attri)te orproperty can )e detected or determined, then the
classi=cation is the ordinal scale. It shold )eemphasi"ed that the ordinal scale implies onlydegrees o# di4erence and does not implymeasra)le amonts o# these di4erences.
%?ample:military ran1
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I2T%R-A* SCA*%
I# an entity can )e measred in sch a way thatnot only the degree o# di4erence )t also theamont o# this di4erence has a meaning, then themeasrement #alls nder the interval scale.
%?ample:
scores in an e?am
temperatre in C
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RATI' SCA*%
In the ratio scale, not only addition ands)traction, )t also mltiplication and division o#o)servation vales are meaning#l.
%?ample:mass
electric charge
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Figure 1. Smmary o# scales o# measrement.
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9R'$%& (R%@$%2C5&ISTRIB$TI'2
Ale? measred the lengths o# leaves on the oa1 tree /tothe nearest cm0:
;,67,68,,6E,6,6,67,E,6F,6>,6,>,F,F,F,7,,6>,6F,6F,67,67,67,67,6
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2ow calclate an appro?imate grop si"e, )y dividingthe range)y how many grops yo wold li1e.
Then rond that grop si"e upto some simplevalue/li1e D instead o# 6.E8 or 5instead o# >.D70.
*et s say we want a)ot F grops. &ivide the range )yF:
6Then rond that p to >.
ic1 a starting vale that is less than or eal to thesmallest vale. Try to ma1e it a mltiple o# the gropsi"ei# yo can.
In or case a start vale o# ma1es the most sense.
/2ote: I# yo dont li1e the grops, then go )ac1 andchange the grop si"e or starting vale and try again.0
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6,6,6,>,>,F,F,F,7,,6>,6F,6F,67,67,67,67,6
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ST%+A2&*%A( *'T
Scores on a test o# physical coordination given to Dstdents:
7; E> FD ;8 76 7< ; D > E D
; 8
Figure 2. Stemand*ea# lot o# Scores on a Test o# hysicalCoordination.
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&'$B*%ST%+ *'TF. D
FK F
7K F < E ;
>
EK E
;. 8Figure . Stemand*ea# lot o# Scores on a Test o# hysicalCoordination.
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9RAHICA* R%R%S%2TATI'2
I% 9RAH
ICT'9RAH
BAR 9RAH
*I2% 9RAH
HIST'9RA+
(R%@$%2C5 '*59'2'9I-% *%SS THA2 C$R-%
'9I-% 9R%AT%R THA2 C$R-%
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I% 9RAH
Movie Freq. (f)
Comedy >
Action F
Romance 7&rama 6
Sci= >
2 G D
Ta)le 8
Favorite T!"e of Movie
Figure #$ (avorite Type o# +ovie
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ICT'9RAH
Figure 5. Pictograph of how many apples were sold atthe local shop over 4 months.
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&'T *'TS
Minutes Freq. (f)
7
6 D
D 8
8 F
> D
F F
7
<
E D
; 8
6
6D 6
2 G >
Ta)le >Minutes to %at Breakfast
Figure &. &ot plot o# mintes to eat)rea1#ast o# > people.
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BAR 9RAH
Fruit Freq. (f)
Apple 8F
'range 8
Banana 6
Liwi#rit DF
Ble)erry >
9rapes F
2 G 6>F
A survey of 145 people revealed their favorite fruit:
Ta)le FFavorite Fruit
Figure '. (avorite #rit o#6>F people.
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*I2% 9RAH
Days Freq. (f)
6 8
D >8 6D
> 6F
2 G 8>
You are learning facts about dogs, and each dayyou do a short test to see how good you are.hese are the results:
Ta)le 7Facts ( )ot Correct
Figure *. (acts I got correcta)ot dogs.
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HIST'9RA+
The #ollowing is the distri)tion o# the nm)er o#meals which 7 real state salespersons chargedas )siness e?penses in a given wee1:
Ta)le < +um,er of Meals of &- .eal State Sales"ersonsCharged
as Business %/"ensesNumer of Meals Freq. (f)
6 67
D 8 DF
> F 68
7 < >
E ; D
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Figure 0. 2m)er o# meals o# 7 real state salespersonscharged as )siness e?penses.
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(R%@$%2C5 '*59'2
$sing the data given )elow, constrct a morethan cmlative #reency ta)le and draw the#reency polygon, less than ogive and more thanogive.
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Mar!s
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*%SS THA2 '9I-%
Mar!s
"umu
lative
Frequ
ency
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9R%AT%R THA2 '9I-%
"umu
lative
Frequ
ency
Mar!s