IAS Maths Notes
Stats 1
, UNIT 1 : MATHEMATICAL MODELLING
1 1 Mathematical models
A mathematical model real-world Situation
simplification
·
is a
of a
It and
can be used to make
predictions forecasts
-
-
A model aims to include all the main
features of real-world
Situations
the world
-
But given the difficulties of real ,
assumptions may be made
when
analysing results
I
Advantages Disadvantages
relatively quick s easy to roduce
simplification of the real-world
· ·
P
cost
·
effective way of analysing Situation can cause errors
the real-world Situation -model doesn't include every aspect
predictions can be made Model work under
·
may only
&
show how changes in variables conditions that
specific are
·
can affect outcomes diffi cult to
implement in the
Situations real-world.
simplify complex
·
1 2 model
Designing a
.
Stage 1 : The
recognition of a real-world
problem
A mathematical model devised
Stage 2: is
Stage Model used make about the behaviour of the
3: to
predictions
real-world
problem
data
Stage 4 :
Experimental are collected from the real world
Stage made devised model
5 :
Companions are
against the
Stage Statistical used test how the model describes
6 :
concepts are to well
the real-world
problem
Stage 7 : model is
refined
, UNIT 2 : MEASURES OF LOCATION AND SPREAD
2 1 .
Types of data
·
Qualitative variables are variables associated with non-numerical data
·
Quantitative variables are variables associated with numerical data
Types of quantitave variables are
-
> Discrete data-takes only specific values in a given range
e number in class
g of girls a
- .
:
> continous data-takes any value in a
given range
-
e .
:
g distance bin two points
.2
2 measures of Central tendency
·
Measures location single value which describes
of is a a
position in a
data set
·
If the single value describes the centre of the data it is the measure
central
of tendency
mode the value/class that occurs more
is
often
>
median is the middle when the data is order
put
> value in
I mean is the value
average
E =
a
Combing means
If A and I
combing of size n mean with B Size 12 mean
-
, 1
of
m +
nzz
F =
ni + Mz
2 3 Other Measures Location
of
.
can be calculated by
-
>
quartiles
>
percentiles
used to the median , quartiles and
Interpolation is estimate
percentiles
·
,
data
-used when is
presented in a
grouped frequency table
this method that the data
evenly distributed
-Using ,
you assume values are
within each Class
Stats 1
, UNIT 1 : MATHEMATICAL MODELLING
1 1 Mathematical models
A mathematical model real-world Situation
simplification
·
is a
of a
It and
can be used to make
predictions forecasts
-
-
A model aims to include all the main
features of real-world
Situations
the world
-
But given the difficulties of real ,
assumptions may be made
when
analysing results
I
Advantages Disadvantages
relatively quick s easy to roduce
simplification of the real-world
· ·
P
cost
·
effective way of analysing Situation can cause errors
the real-world Situation -model doesn't include every aspect
predictions can be made Model work under
·
may only
&
show how changes in variables conditions that
specific are
·
can affect outcomes diffi cult to
implement in the
Situations real-world.
simplify complex
·
1 2 model
Designing a
.
Stage 1 : The
recognition of a real-world
problem
A mathematical model devised
Stage 2: is
Stage Model used make about the behaviour of the
3: to
predictions
real-world
problem
data
Stage 4 :
Experimental are collected from the real world
Stage made devised model
5 :
Companions are
against the
Stage Statistical used test how the model describes
6 :
concepts are to well
the real-world
problem
Stage 7 : model is
refined
, UNIT 2 : MEASURES OF LOCATION AND SPREAD
2 1 .
Types of data
·
Qualitative variables are variables associated with non-numerical data
·
Quantitative variables are variables associated with numerical data
Types of quantitave variables are
-
> Discrete data-takes only specific values in a given range
e number in class
g of girls a
- .
:
> continous data-takes any value in a
given range
-
e .
:
g distance bin two points
.2
2 measures of Central tendency
·
Measures location single value which describes
of is a a
position in a
data set
·
If the single value describes the centre of the data it is the measure
central
of tendency
mode the value/class that occurs more
is
often
>
median is the middle when the data is order
put
> value in
I mean is the value
average
E =
a
Combing means
If A and I
combing of size n mean with B Size 12 mean
-
, 1
of
m +
nzz
F =
ni + Mz
2 3 Other Measures Location
of
.
can be calculated by
-
>
quartiles
>
percentiles
used to the median , quartiles and
Interpolation is estimate
percentiles
·
,
data
-used when is
presented in a
grouped frequency table
this method that the data
evenly distributed
-Using ,
you assume values are
within each Class
