Extensive notes with examples and practice problems ECON10072A Advanced Statistics (ECON10072A)
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Course
ECON10072A Advanced Statistics (ECON10072A)
Institution
The University Of Manchester (UOM)
Boost your understanding of Advanced Statistics with these comprehensive lecture notes! Each concept is broken down with clear explanations, examples, and practical applications. Strengthen your skills with a range of practice problems designed to challenge and enhance your learning, complete with ...
Discrete dala variable of which
: X can only yield isolated values
,
some are often repeated
·
Ordinal : categories have a natural ordering
Bur Charts : firs
& Football league, Premier league the
frequencies and
·
Nominal :
No natural ordering to the categories the relative frequencies
↳ Gende : Male , female
A variable that the of certain
Count
·
:
represents count events
↳ Number of children in household : 0. 1 ,
2
,
3 etc
Continous dala : Variable Y is centinous if it can assure
any value taken from a continuum/interval/rarge of numbers
i height weight incope distribution grash
.
e
,
, government expenditure >
- Histogram : raw data grouped
into intervals &
histyram
=
& find frequery fregers
(a) (fraentr)
relable
,
and dis
Cross-section data : taken at point in time
observation on a
particular variable a
single
for example : anneal Crime figure recorded in 1999, initial salsies of DOM
grads in 2012
, Minterparate & Several cities on a .
single day
Time-series dala : fire
Observation on a
particular variable recorded over a
period of at
regular intervals
for example :
Personal Grime figures in Manchester recorded annually from 1900 -
2022
,
Monthly household expendine on food ,
oil grive over lo years
↳ can be represerved a live
graphs
↳ for daka with different axies -> on excel crak a combo live
gragh with relationship between two variables
Secudey axis steen in the scatter flot
Location Measures : Central location/Cernal Fendency/average
& what a typical value from a set of observations is
& value around which observations in the sample are distributed
.
applicable for continous dala
The Mean :& only
Arithmetic Man = )
= =
. ...
n
adding all values in a sample and dividing this by the sample Size.
Mean of binary variables :
,The I applied
for both continue and discre daca
Median : e finding the middle value of a sampl
Median value Middle value of the data in (smalles to biggest
5Menuvalve
:
set order
organized
tradaa b
ar
Medium doesn't use all data
= less influenced
If dala set is positive skence : Man) Median by outliers
4 If highes value increases - man changes ,
median stays the same
↳ Mean is allded by extreme value skewed
- right
If
*
dala
For
set
symrehic
is
data
regaliely
- mean
skewed
and
: Mean
Median
<Median
are similar M
- - -
2, 6 8, 9 100
, ,
regellin sler
weighted mean : positive Symmetric
S kew
reformulate the arithmetic mean to the following equivalent formula weighted mem :
In
= Wi + we ... twn
=
& = M
+...
= x + x + ....
+ Y
take for of the variables isn't the
& we can't the arithmetic mean certain data types if the size same
alled in the of indes
weighted Mean is used construction numbers
ie - consumer price index (CPE)
↳ eighing calegories differently like food us music
Exable question :
6 , 241
S Pop prop
=
: VE = 9 9 . % = , 0002
0 all
452, 189
11 Poy
=
D : VE = . 0 % Prop = 0 . 02132
WE = 7, 457 , 632
N : 1 % %.
Pop =
Prop = 0 .
3515
6269
G : WE = 16 . 6% pay = 13, 298, 115 Prop = 0 .
Deviation : How much the values in a
saigh differ from one another
range =
largest
-
Smallest
↳ Not ideal due to
cuiliers and
only uses the two extremes
.
Mea
Dispersions from central location : Example where and - =
Sample x Xi di Sargle Y Yi di
I
I 6 2 8 Y
di = xi -
2 3 2 3 I di
I =
j j
-
- -
3 3 3
↳ from the
airhidic mean
-
+ 3 I deciations
observed value -
Mean
, & How for dala set is from the mean
Sample variance :
each
Mean absolute deciatio (MAD) :
E lail = x - >
Mean squared deviation [MSD) : n di = (x -
1)
↳ variance
If dala represents releas population MSD =
Population variance (02)
↳
samyl rainne (c) = (xi -
x) n-1 =
degrees of freed on
values
& Max number of logically independent
S2(x) = (2)3 ( 1)" + 1 13
Example + disadvantages for data :
-
=
variance
-
:
2
-
= (4) + 1 + 1
has interpretation in chir of variance
2
·
vanience no
easy income dala = found
6
& - what is the
2
squared of meaning ?
= 3 to
·
variances for different dala sals are almost impossible compare
( 12 ( - 33
5(y) =
= (4) + -
+
+ (1) + (9)
= (16)
I 13
Standard deciation :
Population standard deviation : 0 = = (xi - ul"
= =
S(xi
standard deviation : S
sanyle n -
1
- 2)
Example :
1 2 7 7 10 , 18
, , , ,
* = 7
S
~
= = ( 6) + ( 5) -
+ (0) + (0) (3)
+ + (832
# (36) + (25) + (9) + (64)
-
= 26 . 8
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