Statistics &
probability
Class Lecture notes
Aqeel Rafique
Statistic:
Statistics is the science of collection, presentation, analysis and interpretation of numerical
data.as well as drawing valid conclusion and making reasonable decision on the basis of such
analysis.
Branch of Statistics:
There are two main branches of statistics.
Descriptive/ Deductive statistics:
This branch of statistics is concerned with the description (collection, presentation, analysis
and interpretation) of numerical data.
Inferential or Inductive statistics:
This branch of statistics is concerned with the drawing conclusion about the population on
the basis of sample information is called inferential statistics.
Population:
Whole aggregate of material about which we need to get some information is called
population.
Sample: (model)
Representative part of the population collected to get the required information about the
population is called sample.
Parameter:
Any numerical value or characteristic calculated from population data is called parameter.
Statistics:
Any numerical value or characteristic calculated from sample data is called statistics.
Inference:
To get result for population after testing sample is called inference.
Data:
Raw fact and figures or the collection of information about any problem under study is
called data.
Types of data:
There are two types of statistical data.
Primary data (initial):
The collection of information that are collected initially from its source and have not gone
through any sort of statistical treatment. It is also called raw data, ungrouped data or first-hand
information.
Secondary data:
It is the data which have already be collected and compile through some sort of statistical
treatment at least once. It is also called grouped data or second hand information.
Presentation of data:
The process of summarizing (Tabular form) and arranging of raw data to get its meaningful
form is called presentation of data. The presentation of data involve following steps.
Classification:
The arrangement of raw data into different classes, group or categories according to some
common characteristics present in the data is called classification.
If the data are classified according to a single common characteristics is called one way
classification. If classified according to two common characteristics called two way classification. And
multi way if more than two criteria of classification is used.
Tabulation:
The process of arranging the data into vertical columns and horizontal rows in a systematics
manner is called Tabulation. The statistical table has at least four parts.
i.
Title
ii.
Box head/ column caption
iii.
Stup/row caption
iv.
Body of the table
Frequency distribution:
The classification of the data into tabular form along with the number of objects in each
class is called frequency distribution.
Variable:
Variable contains different values or change from individual to individual.
Qualitative variable:
Qualitative variable is a variable whose value can never be measured numerically, but can be
expressed as the categories or classes.
e.g.: religion, gender etc.
Quantitative variable:
A variable that can assume numerical value or measurements is called quantitative variable.
There are two types of quantitative variable.
Discrete variable:
It is a variable that can take isolated value or countable values. e.g.: no. of students in a
class, no of families in a house etc.
Counter variable:
A variable which can assume any possible value within an interval or can take measureable
values is called continuous variable.
e.g.: temperature, height, weight etc.
Interval:
The width or size of each class is called interval, denoted by h or I which is obtained by
taking difference of any two consecutive lower or upper limits.
Class boundaries:
These are the actual class limits in which upper limit of first class and lower limit of the next
class are same.
Class marks:
Class marks are the representative value of each class that lies in middle of the classes.
Denoted by X.
Commutative frequency:
It is the sum of the frequencies preceding to a particular class including that class frequency.
These frequencies are used to represent the arrangement of the observations in the distribution.
We can easily trace the position of a particular observation in the distribution.
Graphical representation of data:
Another way to present the raw data into a meaningful form is diagrams or graphs. It is a
visual or pictorial representation of the data.
There are many reasons for drawing graphs the most compelling being that one simple
graph say more than twenty pages of prose. Many graphs just represent a summary of the data that
has been collected to support a particular theory. It is usually suggested that the graphic
representation of data should be looked at before preceding for format statistical analysis.
There are two ways to present the data into visual or pictorial form.
i.
Diagrams or charts
ii.
Graphs
Class
Frequency Class boundaries Class marks Commutative
Interval
(f)
frequency
(c f)
30 - 39
2
29.5 - 39.5
34.5
2
40 - 49
3
39.5 - 49.5
44.5
5
50 - 59
11
49.5 - 59.5
54.5
16
60 - 69
20
59.5 - 69.5
64.5
36
70 - 79
32
69.5 - 79.5
74.5
68
80 - 89
25
79.5 - 89.5
84.5
93
90 - 99
7
89.5 - 99.5
94.5
100
Q. what is the basic difference in diagram & graph?
Q. discuss in detail different types of diagram & graphs, with single example of each.