This document defines key statistical concepts used in data analysis: - Population refers to the total set of items being studied, while a sample is a subset of the population. - There are two types of data: primary data collected by researchers and secondary data previously collected by others. - Variables can be qualitative attributes or quantitative measurements and can be discrete or continuous. - Data is classified by dividing the variable range into intervals called classes, which are defined by class limits and widths. Class frequencies are counted and used to create frequency distributions.

2. Population:
In a statistical enquiry, all the items, which fall within the purview of
enquiry, are known as Population or Universe. In other words, the
population is a complete set of all possible observations of the type
which is to be investigated.
Ex 1 Total number of students studying in a school or college.
Ex 2 Total number of books in a library.
Ex 3 Total number of houses in a village or town.
Sample:
Statisticians use the word sample to describe a portion chosen from the
population. A finite subset of statistical individuals defined in a
population is called a sample. The number of units in a sample is called
the sample size.

3. Type Of Data:
Primary data :
Primary data is the one, which is collected by the investigator himself for
the purpose of a pacific inquiry or study.
Examples(Methods)
1. Direct personal investigation
2. By mailed questionnaire
Secondary data :
Secondary data are those data which have been already collected and
analyzed by some earlier agency for its own use; and later the same data
are used by a different agency.
Examples (Methods)
1. Published report is News papers.
2. Financial data reported in annual repots.
3. Records maintained by the institutions.

4. ATTRIBUTES:
A Qualitative Characteristics like Nationality. Religion, Blood Group,
IQ… ETC is called as an Attribute.
VARIABLE:
A Quantitative Characteristics which can be measured by numbers is
called variable.
eg: Height or weight of an individual, Number of Students in a class.

5. TYPES OF VARIABLE:
DISCRETE VARIABLE:
A variable which can take only isolated values in the given range or is a
set of natural numbers is called Discrete variable.
Eg: Number of Students in a class, Number of phone calls received by a
telephone operator.
CONTINUOUS VARIABLE:
A variable which can take an infinite number of values within a given
range is called Continuous variable.
Eg: Height or weight of an individual, Temperature of a particular city.

6. CLASSIFICATION OF DATA:
The process of arranging data in groups or classes according to their
similarities is technically called Classification of Data.
CLASS:
Most of the discrete or continuous variables are classified by dividing
total range in to number of suitable intervals and each interval represent
Class.
CLASSS LIMIT:
The two Numbers indicating the Class is called Class Limit(Upper limit
and lower limit).

7. CLASS WIDTH:
The Difference between Upper limit and lower limit of a class is called
class width. i.e. Class Width = U.L. -- L.L.
CLASS MARK (MID VALUE):
It is the Mid point of the class interval which is given as:
Class Mark = ( U.L. + L.L. ) / 2
OPEN END CLASS:
The Class having only one limit (i.e. either U.L. or L.L.) is known as
open end class. Eg: Below 20, Above 90.

8. TYPES OF CLASSIFICATION
1. Exclusive type of Classification:
A classification in which the classes are define by excluding upper limit
and including lower limit is called Exclusive type of Classification.
Example: There are 24 students who have secured the marks between 0
and 50. A student who secured 20 marks would be included in class 20-
30, not in 10–20. This method is widely followed in practice.
Eg: 0-10, 10-20, 20-30 ….

9. TYPES OF CLASSIFICATION
Inclusive type of Classification:
A classification in which the classes are define such that both lower class
limit as well as the upper limit of a class is included in that class itself is
called Inclusive type of Classification.
Eg: 1-10, 11-20, 21-30, ……..

10. Method of converting Inclusive to exclusive type of
classification:
For converting data from inclusive form to exclusive form, first of all we
find the half of the difference (gap) of lower limit of that class and upper
limit of the preceding class. Then
New L.L. = Old L.L. – (gap/2)
And
New U.L. = Old U.L. + (gap/2)

11. CLASS FREQUENCY:
The number of observations corresponding to the particular class is
known as the frequency of that class or the Class Frequency. Various
Classes together with their frequencies is called as Frequency
Distribution.
RELATIVE FREQUENCY:
It is defined as the ratio of Class frequency to Total Frequency.
FREQUENCY DENSITY:
It is defined as the ratio of Class frequency to Class Width.

12. CUMULATIVE FREQUENCY DISTRIBUTION:
The cumulative frequency of a class is the total of all the frequencies up to
and including that class. A cumulative frequency distribution is a
frequency distribution which shows the observations ‘less than’ or ‘more
than’ a specific value of the variable.
The number of observations less than the upper class limit of a given
class is called the less than cumulative frequency and the corresponding
cumulative frequency distribution is called less than cumulative
frequency distribution.
Similarly, the number of observations corresponding to the value of more
than the lower class limit of a given class is called more than cumulative
frequency and the corresponding cumulative frequency distribution is
called ‘more than’ cumulative frequency distribution.