Lecture 02 - Chapter 01 - Probability & Statistics by Muhammad Haroon

Probability & Statistics
(Lecture # 02) by
Muhammad Haroon
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Observation
Any information about any field of student is called observation
For example
 Quaid-e-Azam was a good lawyer
 Punjab has 34 district
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Value/Datum
Any numeric observation is called value or datum
For example
 Punjab has 34 district
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Attribute
Any nonnumeric observation is called attribute.
For example
 Quaid-e-Azam was a good lawyer
 Muhammad Haroon is a good teacher
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Data
Set of observation is called data
For example
 Marks of all student in a class
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Quantitative Data
Set of values is called quantitative data
For example
 Marks of all student in a class
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Qualitative Data
Set of attribute is called qualitative data
For example
 Dress color of student in a class
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Statistics
Statistics is study of those methods which are used to collect, present, analyse and
interpretation the data. Statistics is also used in decision making under uncertain
condition. There are two branches of statistics.
 Descriptive Statistics
 Inferential Statistics
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Descriptive Statistics
Descriptive statistics is study of those methods which are used to collect and present the
data.
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Inferential Statistics
Inferential statistics is study of those methods which are used to analyse and
interpretation the data. Statistics is also used in decision making under uncertain
condition.
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Population
A Population consists of the totality of the observations with which we are concerned.
Or
Set of objects or individual having some common characteristics is called population.
For example
 The heights of all the students in the university
 Population of first year student in the university
 Population of piano ball points
 The number of bolts produced by a machine.
N denotes the size of the population.
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Sample
A Sample is the representative part of the population. Sample is studied to know the
properties of the population.
Or
A small part of population which represent all most all characteristics of population is
called sample.
For example
 The heights of all the students in the State class
 Student of 1st year statistics
 Piano ball points at a book shops
The sample size is denoted by n.
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Statistic
Any values calculated from sample data is called statistic (Latin).
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Variable
Any Characteristics which can change is called variable. It is denoted by ( X, Y, Z ) last
capital alphabets.
For example
 Height
 Temperature
 Price
There are two types of variable
 Quantitative variable
 Qualitative variable
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Constant
Any Characteristics which can not change is called constant. It is denoted by ( a, b, c )
first small letters.
For example
 Number of eyes
 Number of hands
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Quantitative Variable
A variable which takes numeric observation is called quantitative variable.
For example
 Height
 Temperature
 Price
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Qualitative Variable
A variable which takes nonnumeric observation is called qualitative variable.
For example
 Name
 Shirt color
There are two types of Qualitative variable
 Discrete Variable
 Continuous Variable
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Discrete Variable
A variable which takes specific values is called discrete variable.
For example
 Number of Chair
 Number of student
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Continuous Variable
A variable which takes all possible values is called continuous variable.
For example
 Height
 Time
 Temperature
 Weights
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Order Statistics/Array
The arrangement of values in either order is called order statistics. There are three
meaning of statistics
 Statistics in plural sense
 Statistics in singular sense
 Statistics as plural of statistic
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Statistics in Plural Sense
The word statistics in plural sense are the numerical observations collected for some
definite purpose regarding to some field of study.
Or
Statistics is name of a subject.
For example
 The ages of students are called the statistics of ages
 The prices of fruits collected are called as statistics of fruit prices
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Statistics in Singular Sense
Statistics in singular sense is a body of methods used in the collection, presentation,
analysis & the interpretation of data.
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Statistics as Plural of Statistic
Any values calculated from sample data is called statistic. When we have more than one
statistic, then we shall use the word statistics as plural of the word statistic. Thus the
sample mean ( 𝑋 ) and the sample standard deviation ( S) are the statistics.
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Census
The study of population is called census.
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Sample Survey
The study of sample is called sample survey.
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Error
Difference between estimated value and actual value is called error.
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Primary Data (with respect to collection)
Such data which is collected from field and present in its original form is called primary
data.
For example
 Marks of students obtained of class
It is also called data, unarranged data, ungrouped data, raw data and firsthand collected
data
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Secondary Data
Such data on which at least one statistical method is applied. It is also called grouped
data.
For example
 Marks of students obtained from office record
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Ratio
Ratio is defined as “Fraction of two number”.
For example
 Ratio of “a” to “b” = a:b = a/b
 Ratio of students with uniform to without uniforms
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Fraction/ Proportion
Fraction is ratio of a part to its total
For example
 Part : Total = Part/Total
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Model
A model is a mathematical statement used in studying the results of an experiment or
predicting the behavior of future repetitions of the experiment. A set of observations can
be described by means of simplest model as given below.
𝑌𝑖 = 𝜇 + 𝜀𝑖
In the above model, 𝑌𝑖 represents the individual observations, 𝜇 denotes the population
means and 𝜀𝑖 denotes random error.
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Random Error
The random error 𝜀𝑖 is a chance variation in the observational process. The random error
may be written as 𝜀𝑖 = 𝑌𝑖 - 𝜇 , 𝜀𝑖’s are usually assumed to be from population having zero
mean, while the term 𝑌𝑖 - 𝜇 is known as deviation of an observation 𝑌𝑖 from population
means ( 𝜇 ).
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Factorial (!)
“n” Factorial is the product of n positive integers (!) is by n!.
For example
 0!=1
 2!=2x1=2
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Summation Notation
Summation notation is used for sum of Values. It is denoted by .
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Notations
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Notations
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End
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Lecture 02 - Chapter 01 - Probability & Statistics by Muhammad Haroon

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Lecture 02 - Chapter 01 - Probability & Statistics by Muhammad Haroon