Introduction to Statistics

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Functions or Uses of Statistics:
Statistics simplifies complexities,
Statistics presents facts in a definite form,
Statistics simplifies comparison of data,
Statistics studies relationship among different facts,
Statistics studies changes in the level of a given phenomenon,
Statistics aids forecasting,
Statistics guides the formation of policies, and
Statistics tests the laws of other sciences.

Limitations of Statistics:
Statistical results are true only on the average or in the long run,
Statistics does not deal with facts which cannot be numerically measured,
Statistical results may be sometimes, due to poor collection of data,
fallacious and misleading,
Only experts can handle the statistical data efficiently, and
Statistics provides only the tools for analysis. It cannot however
change the nature of the causes affecting statistical data.

Collection of Data:
There are two sources of collecting data:

Primary Sources: The data published or used by an organisation which
originally collects them are called ‘primary data’. The data in the
Population Census reports are primary because they are collected,
compiled and published by the Population Census Commission.
Secondary Sources: The data published or used by an organisation other
than the one which originally collected them are known as ‘secondary
data’. For example, the data in Economic Survey of Pakistan.

Methods of Collection of Primary Data:
Direct Personal Observation, i.e., through individual interviews.
Indirect Oral Investigation, i.e., on evidence of persons or parties
suppose to know the facts directly or indirectly.
Registration is the most popular method of collecting data.
Estimates Through Local Correspondents is not a formal collection of
data. This method is generally used in crop or land estimates.
Investigation Through Enumerators to get the forms of inquiry filled in
from the informants.
Mailed Questionnaire Method.

Methods of Collecting Secondary Data:
Official Sources, i.e., publications of Federal Bureau of Statistics;
Ministries of Finance, Trade and Industry, Telecommunication, Education,
etc.
Semi-Official Sources, i.e., publications of State Bank of Pakistan,
SECP, District Councils, Municipal Committees, etc.
Private Sources, i.e., publication of trade associations, Chamber of
Commerce and Industry, etc.
Technical and Trade Journals.
Research Organisations, i.e., universities, Institute of Education and
Research, Institute of Development Economics, etc.

Variable and Constant:
A measurable quantity which can vary from one individual to another is
called a ‘variable’. Examples are heights and weights of students in a
class, prices of commodities, number of children in a family, etc. It is
denoted by the last letters of alphabets, i.e., x, y, and z.
‘Constant’ is a quantity which can assume only one value. Examples are (
= 3.14159, e = 2.71828, etc. It is usually denoted by the first letters
of alphabets, i.e., a, b, c, d, …

Continuous or Discrete Variables:
A variable which can assume any value within a given range is called a
continuous variable. For example, the heights and weights of students,
temperature, speed, etc. the height of a student can be 62”, 62.5” or
62.45”.
A variable which can assume only some specific values within a given
range is called a discontinuous or discrete variable. For example, the
number of houses in a town, number of children in a family, number of
students in a class, etc. a discrete variable takes on values which are
integers or whole numbers like 0,1,2,3,4,5, … but cannot be 2.5, 3.3,
3.91, 14.235, etc. There cannot be 4.5 houses in a town or 10.15 number
of students in a class, etc.

Quantitative and Qualitative Data:
Quantitative variables are heights, weights, temperature, speed, etc.
Qualitative data are described by qualitative variables, such as marital
status, religion, colour, race, etc.

Errors of Measurement:
The difference between the measured value and true value is called the
error of measurement. These errors are of two types:

Compensating Errors: are the errors which tend to balance or cancel out
in the long run are called ‘compensating errors’ or ‘chance errors’ or
‘random errors’.
Biased Errors: are the errors which tend to occur in the same direction
and have cumulative in effect, are called ‘biased errors’ or ‘cumulative
errors’. Such errors are arised from faulty instruments or personal
intentions.

Classification of Data:
The process of arranging data into classes or categories according to
some common characteristics present in the data is called
‘classification’.

Data can be classified by many characteristics, but there are four main
bases of data classifications, there are:

Qualitative, i.e., sex, religion, marital status, race, etc.
Quantitative, i.e., height, weight, income, etc.
Geographical, i.e., continents, states, cities, etc.
Chronological, i.e., arrangement of data by their time occurrence, e.g.,
date of birth, date of joining, etc.

Types of Data Classifications:
Data can be classified by one, two or more characteristics at a time:

Quantitative:
One-way: when data are classified by one characteristic.
Two-way: when data are classified by two characteristics.
Three-way: when data are classified by three characteristics.
Many-way: when data are classified by many characteristics.

Qualitative:
Two-fold or dichotomy: we may divide a characteristic into two sub-
classes one possessing the characteristic and the other not possessing
it. For example, the literacy and illiteracy of a country.
Three-fold or trichotomy: when data are classified into three sub
classes.
Manifold: when data are classified into many sub-divisions.

Frequency Distribution:
Frequency Distribution of Discrete Data: There are no class boundaries
because discrete data are not in fractions. If class interval size is
one we usually take single values.

No. of children in a family Number of
families 0 7 1 3 2 25 3 16 4 9 5 4 6 1 Total 65
Frequency Distribution of Continuous Data: Class boundaries are formed
for continuous data because the continuous data are in fractions:

Heights of students in a class (inches) Number of students 55.5-
58.0 1 58.0-60.5 6 60.5-63.0 17 63.0-65.5 18 65.5-68.0 18 68.0-
70.5 4 70.5-73.0 1 Total (( f) 65
Cumulative Frequency Distribution: is the table showing cumulative
frequencies:

Heights (inches) No. of students
Less than
Cumulative
Frequency Heights (inches) No. of students
Greater than
Cumulative
Frequency Less than 55.5 0 55.5 and more 65 Less than 58.0 1 58.0 and
more 64 Less than 60.5 7 60.5 and more 58 Less than 63.0 24 63.0 and
more 41 Less than 65.5 42 65.5 and more 23 Less than 68.0 60 68.0 and
more 5 Less than 70.5 64 70.5 and more 1 Less than 73.0 65 73.0 and
more 0
Relative Frequency Distribution: is expressed in percentage of frequency
to total frequency:

Heights Frequency
(No. of students) Relative frequency
(%) 55.5-58.0 1 1 / 65 × 100 = 1.54 58.0-60.5 6 6 / 65 × 100 =
9.23 60.5-63.0 17 26.15 63.0-65.5 18 27.69 65.5-68.0 18 27.69        68.0-
70.5 4 6.16 70.5-73.0 1 1.54    65 100
Relative Cumulative Frequency Distribution:

Heights
(Inches) No. of students
Less than
Cumulative
Frequency Relative
Frequency Heights
(Inches) No. of students
Greater than
Cumulative
Frequency Relative
Frequency Less than 55.5 0 0 55.5 and more 65 100 Less than 58.0 1 1 /
65 × 100 = 1.54 58.0 and more 64 98.46 Less than 60.5 7 7 / 65 × 100 =
10.77 60.5 and more 58 89.23 Less than 63.0 24 36.92 63.0 and
more 41 63.08 Less than 65.5 42 64.61 65.5 and more 23 35.38 Less than
68.0 60 92.31 68.0 and more 5 7.69 Less than 70.5 64 98.46 70.5 and
more 1 1.54 Less than 73.0 65 100 73.0 and more 0 0
Bivariate Frequency Distribution: involves constructing frequency
distribution of two variables:

Weights
(pounds) Heights (inches)  57-59 60-62 63-65 66-68 69-71 72-
74 Total 100-104 3 7 - - - - 10 105-109 - 5 10 2 1 - 18 110-
114 1 1 4 6 4 0 14 115-119 - - 1 1 4 2 8 Total 3 12 15 9 9 2 50
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Description: bank reconcilation statement,circular flow of income, closing enteries, coefficient of correlation, concepts of National income, Consumption Functions, Determination of National income,Financial statement, Flow of Funds accounts, Index numbers, Introduction to statistics,investment, macro economics, measures of central tendency, measure of depersion, measure of shape distribution, merchandise inventory, micro macro economics, Micro Economics, multiplier and accelerator, probability, public finance, random variable,regression,sample distribution theory, statistics dynamics and comparative, theofy of employment, trade cycle