Introduction to Statistics - Summary - 2019

Introduction to
tSgGao
Statistics

,Lecture A -
INTRODUCTIONTOSTATISTK.SI -




-
Statistics is the study of the collection , organization ,
analysis ,



interpretation and presentation of data


-


Descriptiuestah.sn#
→ use : quantitatively summarizing information I data


-

Inferential
→ use : make inductive inferences from data C a sample ) to a more

general situation Ca population )
#




-
R#s Notation :




-
site's
→ x or y


-




QXfyingkandOMHe-fourcumulah.ve/evels-

also has the of
level properties
→ the
each

previous levels




!
→ the measurement level of a random

variable determines which analyses you

Should Or shouldn't perform on it



-

Nominalvariable.SI Nominal variables




÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷ :÷÷÷÷÷÷ :÷÷÷÷÷÷÷÷÷÷÷÷÷÷


2-
→ e -
G .
age categories : g -
13 , 14-18 ,
1g -
30 ; O , 1,2 There is a meaningful
ordering in the outcomes

, -

invariables Interval Variables
→
e.g .
temperature in
degrees Celsius l .
Assign mutually exclusive




:* :
→




÷÷÷÷÷÷÷÷÷÷ ÷÷÷÷÷÷÷÷÷:
3. The intervals between each

of the ordered outcomes is


meaningful and the same size .




-

ratiouariab.ie# Ratio Variables
→ e. g. dosage in milligram :
Omg , 1mg , 2mg ;
1 . Assign mutually exclusive




÷÷÷÷÷÷÷÷÷ :c : %:
:÷÷÷÷÷÷÷÷÷÷÷
each of the ordered outcomes is


and the size
meaningful same .




4
' '
"

.
Absolute zero point : A zero


means that there is ab sense of that


variable .




' :÷÷÷÷÷÷÷÷÷÷÷÷÷f÷÷÷
÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷ :÷÷÷÷÷÷÷÷

→ e .
g .

age rounded to whole years


-

continuousrandom-anab.es Note :



→
t.naen.se
.

: :: then :* : : ÷÷÷÷÷÷÷÷÷÷÷÷÷÷
( which could also be -
as to to )
→ e in Corot )
.
g .



age years rounded
→ e.g .
me of alcohol consumed

→ e .
g .


dosage C not
categories )
→ e .

a -


gender scales C feminine to masculine )




-

,-


tryvs.probabiityD-itribuh.cn s -




Fr#Cy C of outcome )
-
an


→ How times
many a certain outcome occurs

→
trequencydistribuh.co#
↳ a table or a graph that shows for each outcome how times it
many occurs



-


probability
→
the relative frequency of that outcome

↳ how many times the outcome occurs out of the total number of
observations
→ probabilityD.is/-ribuh0#
↳ show the probability for each Outcome of a random variable
↳
probabilities always add up to i




#

-



D-esqestah.SI -




"
"
-

Statistics for describing TQ
#
describing
" " ' ' "
→ the center or typical Vallee

of a variable

→ mode ,
median , mean



for
"
Statistics
"


describing Dispersion
-




→
describing the variation , speed , dispersion
in the scores

standard deviation




:/
→
range .
variance ,




:
÷÷÷÷÷÷÷÷÷÷÷÷
Median
-




→ the value higher half from
separating the the

lower half of the data

→ 50% of the data is above and the median
below

value


-


Mean Population :



→ add up the values of all our observations for our
µ =
E#
N
variable X
¥qzqn①
worn ,
? III. Img ; ggnobseruanons
→
thesumofthedeviahonbetweenthemeanan#




theobseruaricnsisalwaysoll

, -



Disposure -




Range
-




→ the difference between the variable 'S

largest and smallest value


-


Variance Population :



→ the
average squared deviation from
•
z=EY)2
the mean .
N
/
↳ "

: : : : : .in : : : :::
es




I


-
standarddeuiah.co# Population :



→ the s " " " " ° " " the " " "




Sample
ms:cxM
°=£M=%⇐NT :




n - i



#




Lecture 2
-


P#iityDitbuhon -




-


probability
→
the relative frequency of that outcome

↳ how many times the outcome occurs out of the total number of
observations
→ probabilityD.is/-ribuh0#
↳ show the probability for each Outcome of a random variable
↳
probabilities always add up to i




-


D-bcreteprobatsilitydistoibuh.cn# Notation :




I Essie :
"
: Futuna
is %EEokE
. on me x. axis


Rules :



A -
A probability always lies

.




I


:÷÷÷÷÷÷÷÷÷÷÷:i
PCA or D) =
PLAIT PCB )
4 .
Complement rule :



PCA ) = 1 -
PC NOT A )
5. For NON mutually
exclusive
-




events a and B :


PCA or B) = PCA ) t PCB ) -
PCA and B )