Elements Of Statistics

1
Elements Of Statistics

• In Summation Notation

2
Algebraic Mean

• In Summation Notation

3
Summation Notation
4
Algebraic Mean

• In Matrix Algebra Notation

5
Matrix Algebra Notation
6
Matrix Algebra Notation
(11)(12)(13)(14)(15) 15
7
True Variance

• In Summation Notation

8
Summation Notation
9
True Variance

• In Matrix Algebra Notation

10
Matrix Algebra Notation
11
Matrix Subtraction X X
12
Pairwise Differences
13
Triangulate the Matrix
14
Square the Matrix Elements
15
Variance
Sum the squared elements
Relational space
16
Covariance

• In Summation Notation

17
Summation Notation
18
Covariance

• In Matrix Algebra Notation

19
Matrix Algebra Notation
20
Obtained Scores
21
Deviation Scores
x
y
22
Variance
xx
yy
23
Covariance
xy
yx
24
Correlation

• In Summation Notation

25
Summation Notation
26
Correlation

• In Matrix Algebra Notation

27
Matrix Algebra Notation
28
Obtained Scores
29
Standard Scores
Zx
Zy
30
Correlation Matrix
31
Correlation Matrix
ZxZx
ZxZy
ZyZy
ZyZx
32
Correlation Matrix