The document outlines various statistical concepts including data types (nominal, ordinal, interval, and ratio), measures of central tendency (mean, median, mode), and variability (variance, standard deviation). It discusses the application of Chebyshev's theorem, the empirical rule, and concepts of covariance and correlation. Additionally, it covers permutation and combination principles, as well as Bayes' theorem in probability.

1. Variables
:#
of columns .
skewed left :
median > mean
observations
:#Of rows •
z
-
score :
.
nominal :
labels
zi =
×i -
I
.
ordinal :
ranking
s
.
interval
:# ,
0 doesn't matter
.
Chebyshev 's Theorem :
At least
.
ratio :#
,
zero matters ( I -
z÷ ) of data values must be
.
relative freq .
= ¥9
'
Within ± zstd .
dev .
of the mean
.
percent freq .
= fr#
'
×
100.1 .
•
Empirical Rule : 681 .
Wlih 1 Stolidly
.
sample mean : It
× 't×z+ .
. .×n 95% Wlih 2 ,
99.71 . Wlih 3
n
.
population covariance :
.
Population mean
:µ=×=×2tI×no×y=
E ( Xi
-
Mx )( Yi -
My )
N N
.
Weighted mean
:I=€w-i××
•
sample covariance :
if Wi
s×y=
E ( Xi -
F) ( yi
-
g )
.
Outlier : 1. SIQR or 2- score
n -
I
I 131
°
If Sxy > 0 :
POS rel .
, Sxyc 0 :
neg .
.
median : middle rel .
, s×y=O : no re
.
mode :
Most
•
population Correlation :
'
Compute pth percentile Cxy =
8××8y
-
i = ( do )n
•
permutation :
order matters ;
-
if i is not integer →
roundup PF :¥s :
-
if i is
integer , avg . of xid
°
Combination :
order doesn't
Xiii matter ;
Cnr =
rein
.
1QR=Q3 -
QI
•
U =
"
Or
"
Population variance : on =
"
and
"
g2=
IF ( xi
-
M )2 .
PCA ) +
PCAC )=|
N .
PCAUB )=P( A) + PC B )
-
PCANB )
•
sample variance :
•
Mutually exclusive : PCANB )=O
sz =
I. ( xi -
E)
2
.
PCAIB ) = PIES,B
'
n -
1
.
PC An B) =
PCB ) .
PCAIB )
°
standard deviation : =
Pla ) .
PCBIA )
not or is •
independent events : PCAIB )=P( A )
°
coefficient of Variation : ↳ PCANB )=P( A ) .
P ( B )
( ✓ =
standard dev .
× 100%
•
PC B) =
FPCBIAI ) PCAI )
mean °
Bayes
'
Rull
PC A. 1
B) =
P
!LBTB
)
=
PCBIA , )p( A ,
)
•
Skewed right :
Mldh ) Median PCBIA ,
) PLA ,
]+PLBlA2)PLAz )
•
PC B) =P ( BIA ,
)P( A.) + PCBIAZ )P( Az )