1. Inferential statistics allows geographers to make generalizations about populations based on samples. It enables them to handle large datasets and determine relationships between variables. 2. Models are simplified representations of reality that can be physical or symbolic. Physical models visually depict systems while symbolic models use mathematical symbols. 3. Models have advantages like enabling experimentation at low cost but also limitations since they are simplifications and may not accurately represent changing realities over time.

1. SAINT AUGUSTINE UNIVERSITY OF TANZANIA
BUKOBA CENTRE
FACULTY: EDUCATION
DEPARTMENT: GEOGRAPHY
COURSE TITLE QUANTITATIVE TECHNIQUES IN GEOGRAPHY
COURSE CODE: GE 244
NAME OF INSTRUCTOR: MR, BASHEKA J. J
WORK: GROUP ASSIGNMENT
DATE OF SUBMISSION: December 2013
GROUP NAME SOPHISTS B
PARTICIPANTS
NO NAME REG NO SIGNATURE
1 KIBIRITI JOSEPH BAED II 41546
2 LAMECK MHOJA BAED II 41554
3 MADUHU GONZI BAED II 41573
4 MAPESA NESTORY BAED II 41584
5 MATHIAS BHOKE BAED II 41594
6
Question 4
a/ Why do we make inferences in geographical studies
b/ Explain the meaning, functions, limitations and characteristics of models in geography.

2. Inferential statistics consists of generalizing from samples to populations, performing
hypothesis testing, determining relationships among variable and making predictions. ( Bluman
1976).
Statistical Inferences: Sampling theory uses statistical underpinnings to make a generalized
statement about a specific population extended from the studies conducted.
Therefore Inferential statistics is the type of statistics which deals with methods that enable a
conclusion to be made from a sample of observation that describe the property of the population
from which the sample was drawn also this type known as Quantitative method. Inferential
statistics originated in the 1600’s when John Graunt published his book on population growth
Natural and Political Observations. Made upon the Bills of Mortality at the same time
mathematician/ astronomer, Edmund Halley published the first complete mortality tables.
Sampling techniques for inferential statistics include Testing of hypothesis and Probability
theories. In testing hypothesis means to state on the basis of data the researcher has collected
whether or not the hypothesis seen to be valued. The main question is to accept the null
hypothesis or to reject it.
The significance level correspond to the confidence level
CONFIDENCE LEVEL SIGNIFICANCE LEVEL
90% 0.1
95% 0.05
99% 0.01
WHY DO WE MAKE INFERENCES IN GEOGRAPHICAL STUDIES
There are various purposes and reasons to make inferences in Geographical studies. Such
benefits are as follows below;
It enables geographers to handle large quantities which can be easily summarizing information
of large number of data.
They are simple to understand and easy to apply also do not require any assumption to be made
about population following normal or any other distribution. when the sample sizes are
small.Example; Non-parametric tests are distribution free. Most non-parametric tests do not require

3. Lengthy and laborious computations and hence are less time-consuming. If significant results are
obtained no further work is necessary.
Measurement techniques help in maintaining objectivity of study. In geographical research as
more and more scales of measurement are being developed, objectivity of study is increasing.
Even if several factors contribute in hindering such objectivity, it has been achieved to such a
limit that useful prediction has been possible.
To determine the normal distribution;The most common probability distribution is the normal
distribution. The normal distribution is a continuous distribution that is symmetric and bell-
shaped.
Its tool can be used to draw conclusions. The process of data to create models and be of use
relies heavily on this process and thus its importance to make inferences in geographical studies.
Mathematical Notation,The mathematical notation used most often in statistical
inferences used in geography example is the summation notation.The Greek letter is used
as a shorthand way of indicating that a sum is to be taken:
ni
i
i
x
1

4. To determine the total area; Inferential statistics in Geography used to determine the total area
under the curve is equal to one.
The method can be used in other subjects, they convert data into mathematical from then
making comparison with variable, formulating principles hence they used to test the significance.
CONCEPT, CHARACTERISTICS ,FUNCTION AND LIMITATION OF MODEL IN
GEOGRAPHY
Chorley and Haggett (1967) defined model is a simplified structuring of reality that presents
supposedly significant features of relationships in general form.
Thus “model’’ is conventionally used in a number of different ways. In its simplest form a
model is the representation of reality in an idealized form. The process of model building is
actually a process of idealization.
TYPES OF MODELS
There are two classes of models that are commonly used in research activities, classified as
follows:
a) Physical Models (b) Symbolic Models
PHYSICAL MODELS
These types of models give the appearance of the real system, as such, these include toys
and photographs. These models easily depict the system but are not easily manipulated.
This makes them of little value for purpose of analysis and prediction. Physical models
are the least abstract of all models. These are of two subtypes:

5. a/Iconic models: Iconic models represent the system as it is but in different size. Thus Iconic
models are obtained by enlarging or reducing the size of the system. In other words, they are
images. Some common examples are photographs, drawing, model airplanes, ships engines
globes, maps etc. A toy airplane is an iconic model of a real one. Iconic models of the sun and its
planets are scaled down while the model of the atom is scaled up so as to make it visible, to the
naked eye,
Figure 1 GLOBE Figure 2 MAP
b) Analogue Models: In analogue models one set of properties is used to represent another set of
properties. After the problem is solved the solution is re-interpreted in items of the original
system.
For example, contour lines on a map are analogue of elevation as they present the rise and fall of
heights. Graphs are analogues as linear lines are used to represent a wide variety of variables
such as time, percentage weight and others.
SYMBOLIC MODELS
In this class models, letter, numbers and other types of mathematical symbols are used to
represent variables and the relationships between them. Thus symbolic models are some kind of
mathematical equations or inequalities reflecting the structure of the system they represent.
Inventory models, queuing models etc. are the example of symbolic models. The symbolic
models are the most abstract models and, therefore, usually general in nature. Symbolic models
can be manipulated easily and, therefore, of great value for analysis and prediction. Hence, in
research symbolic models are often used.
Quadratic Equation

6. Symbolic models have following subtypes:
Mathematical Models: Sometimes, models described by means of mathematical symbols and
equations are known as mathematical models. For example, simulation model uses mathematical
formulae. This model is very commonly used by the manager to „simulate‟ their decision
making process.
Function Models: Models may also be grouped according to the mathematical function used.
For example, a function may serve to acquaint the analyst with growth pattern of consumer
demand.
Quantitative Models: are those models that can measure the observations. A yardstick, a unit of
measurement of length value, degree of temperature, etc. are quantitative models. Other example
of quantitative models are the transformation models that help in converting a measurement of
one scale into one of the other scales (e.g. Logarithmic tables, Centigrade vc. Fahrenheit
conversion scale) and the test models that act as „standards‟ against which measurements are
compared (example., a specified standard production control, business dealings, the quality of a
medicine).
Qualitative Models: are those that can be classified by the subjective description in terms of
numeric data. Examples of these are the “economic models” and the “business models” which
represent the gathering and representation of data pertaining to economic or business research
problem respectively.
Heuristic Models: These models are mainly used to explore alternative strategic (course of
action) which have been overlooked previously, using mathematical models to represent systems
that define strategies.
CHARACTERISTICS OF GOOD MODELS
i) It should be capable of adjustments with new experimental situations without having any
significant change in its framework
ii) It should contain limited variables.
iii) A model should not consume too much time in its construction
iv) Model are structured in the sense that the selected aspect of the web of reality are exploited
in term of their connections.
v)Model are analogies because model are different from the real world ,the use hard ware model
is an obvious example of the general aim of model builder to reformulate some features of the

7. real world into a more familiar, simplified, accessible, observable , easily formulated or
controllable form.
vi) It regards as experimentally fertile, suggesting further questions .
vii) They are sought of as selective pictures and direct description of the logical.
.
ADVANTAGES OF A MODEL
Models play a very important role in geography.
i)Models simulate descriptions and explanations of the operations of the system that they
represent. By experimenting with models one can determine how the changes in the conditions
will affect performance of a system.
ii)Models enable us to experiment in a cost effective manner than the system itself which is
either impossible or too costly.
iii) It depicts a research problem much more precisely.
iv) It provides a logical and systematic approach to the research problem.
v) It indicates the limitations and scope of the research problem.
vi) It presents the overall structure of the research problem more comprehensively.
vii) It facilitates dealing with the problem in its totality.
viii) It enables the use of mathematical techniques to analyse the research problem.
ix ) Analogue models are easier to manipulate than iconic models.
FUNCTIONS OF MODELS IN GEOGRAPHY
Based on various properties and uses of a model it is nine (9) functions maybe identified ;
Acquisitive or Organizational, The model provides a frame work where in the information may
be defined, collected, ordered and manipulated. A model acquires the information that could be
defined in its frame work or provides a frame work for defining certain kind of information.
Logical; A model explain the situation rationally accounting for how a particular phenomenon
comes about or how a particular relationship among components parts work about.
Psychological; it can act as a psychological device that facilitates complex interaction to be
more easily visualized , a kind of picturing device . This function enables some group of
phenomena to be visualized and comprehended more easily that could otherwise not be because
of its magnitude and complexity. A model help to understand the reality in a simpler manner
than otherwise it would have been.

8. Normative; the model represents reality in an Idealized form with the help of certain norms,
conditions assumption. The normative function of a model allows broad comparisons to be
made, by comparing some less known phenomena with more familiar ones.
Systematic; It function like a system, the systematic of a model stresses that the “web of reality”
should be viewed in term of interlocking system. This leads to the constructional function of the
system.
Constructional; It means that a model provides a stepping –stone to the building of theories and
laws. As a constructional device it helps in searching for geographic theory or the extension of
the existing theory.
Selective;it is a selective approximation, allowing some fundamental, relevant or interesting
aspects of the real world to appear in some generalized form.
Interpretative;an important function of the model is to provide an interpretation of the theory in
the sense that every sentence occurring in the theory is a meaningful statement.
Cognitive;finally there is the cognitive function of model, promoting the communication of
scientific ideas.
LIMITATIONS OF MODELS IN GEOGRAPHY
Models have few disadvantages which are as follows:
i) Models are an attempt in understanding a research problem and should never be considered an
absolute ever.
ii) The validity of any model with regard to the research problem at hand can only be verified by
carrying out experiments and by characteristics of data thus obtained.
iii) Analogue models are less specific and less concrete
iv) These are difficult to manipulate for experimental purposes
vi) It is not easy to make any modification or improvement in these models.
vii) Adjustments with changing experimental situations cannot be done in these models.
In conclusion; inferential statistics is body of technique used to assess the degree of certainty
with which a statement can be made about a population is studied or has been studied. It is
classified into two main groups basing on whether the data is normally or not normally
distributed. The scales for measurements are like Nominal scale, Ordinal scales, Interval scale
and Ratio scale. Also models provide controls for the model and solution a model once accurate
may cease to represent reality or the variables believed to be beyond control may change in value
or the relationships of variables may change, provision must be made for control of the model
and the solution as applied in geographical studies.

9. REFERENCE
Beri, G.C. (2009). Business Statistics, 3rd
Ed. Tata McGraw Hill Pvt. Ltd.; India.
Cooper, Donald R. & Schindler, Pamela S. (2006). Business Research Methods, Tata McGraw
Hill Companies; India.
Kothari, C.R. (2004). Research Methodology Methods and Techniques, New Age International
(P) Limited: New Delhi.
Singh, D. & Chaudhary F.S. (2006). Theory and Analysis of Sample Survey Designs, New Age
International (P) Limited: New Delhi.
Shajahan, S. (2009). Research Methods for Management, Jaico Publishing House, Delhi; India.