This document discusses different types of data classification and frequency distributions. It defines raw data and explains the objectives and types of classification, including chronological, spatial, quantitative, and qualitative. Variables are classified as continuous or discrete. A frequency distribution arranges raw data into classes and shows the frequency of observations in each class through tables or arrays. The key elements of a frequency distribution like class limits, midpoints, and intervals are also explained.

2. RAW DATA
The unclassified data is called raw data
CLASSIFICATION OF DATA
The process of grouping data according to their
characteristics is known as classification of data
Objectives of Classification:
a] To simplify complex data
b] To eliminate unnecessary details
c] To help comparison
d] To make analysis and interpretation easy.
e] To arrange the data according to their common
characteristics

3. TYPES OF CLASSIFICATION
CHRONOLOGICAL
CLASSIFICATION
SPATIAL
CLASSIFICATION
QUANTITATIVE
CLASSIFICATION
QUALITATIVE
CLASSIFICATION

4. Chronological organization:
The organization based on time is called chronological
organisation.The chronologically organised data is called
time series. Example- Year, month, week, day etc
• Spatial or Geographical organisation
The data are classified with reference to geographical
locations such as countries, States, cities, districts ,etc.
• Quantitative organisation:
The data organised with reference to quantities are called
quantitative classification. Example, height, weight, age,
income, marks of students, etc.,
• Qualitative organisation:
The data organised with reference to qualities are called
qualitative classification. Example, nationality, literacy,
religion, gender, marital status, etc

5. VARIABLES:
variables are anything their values are changing.
They are broadly classified into two types.
1. Continuous variable
2. Discrete variable
A continuous variable can take any numerical value. It
may take integral values (1, 2, 3, 4, ...), fractional values
(1/2, 2/3, 3/4, ...), and values that are not exact
fractions.(eg. height, weight, mark etc)
A discrete variable can take only certain values. Its value
changes only by finite “jumps”.(eg. Number of children in
a family, number of books in a library etc

6. FREQUENCY DISTRIBUTION
A frequency distribution is a comprehensive way to
classify raw data of a quantitative variable. It shows how
different values of a variable are distributed in different
classes along with their corresponding class frequencies.
CLASS FREQUENCY
0-10 1
10-20 3
20-30 5
30-40 1
40-50 2

7. CLASS LIMITS
Each class in a frequency distribution table is bounded by
Class Limits. Class limits are the two ends of a class.
The lowest value is called the Lower Class Limit and the
highest value the Upper Class Limit.
Example :10-20 here 10 is lower limit and 20 is upper limit
MID-POINT
The Class Mid-Point or Class Mark is the middle value of a
class. It lies halfway between the lower class limit and the
upper class limit of a class.
Class Mid-Point or Class Mark = (Upper Class Limit + Lower
Class Limit)/2

8. CLASS INTERVAL
Class interval: Difference between upper limit and lower limit
Class interval=upper limit-Lower limit
Example 10-20
Class interval=20-10=10
FREQUENCY
Number of items [observations] falling within a particular
class.

9. while preparing a frequency distribution ,the following four
questions need to be addressed
• How many classes should we have?
• What should be the size of each class?
• How should we determine the class limits?
• How should we get the frequency for each class?
• How many classes should we have?
Number of classes can be the calculated by dividing the
range (the difference between the largest and the smallest
values of variable) by the size of the class intervals.

10. • What should be the size of each class?
Given the range of the variable, we can determine the number
of classes once we decide the class interval.
Thus, we find that these two decisions are interlinked. We
cannot decide on one without deciding on the other.

11. • How should we determine the class limits?
The lower and upper class limits should be determined in
such a manner that frequencies of each class tend to
concentrate in the middle of the class intervals.
Class intervals are of two types:
(i) Inclusive class intervals: In this case, values equal to
the lower and upper limits of a class are included in the
frequency of that same class. . Here upper limit of a class
and lower limit of the next class are not same
(ii) Exclusive class intervals: In this case, an item equal to
the upper class limit is excluded from the frequency of that
class. Here upper limit of a class and lower limit of the next
class are same

12. EXCLUSIVE INCLUSIVE

13. • How should we get the frequency for each class?
Frequency of an observation means how many times
that observation occurs in the raw data. The counting of
class frequency is done by tally marks(/) against the
particular class. The counting of tally is made easier when
four of them are put as //// and the fifth tally is placed
across them as ////

14. Prepare a frequency distribution from the following
data by using exclusive method
2,4,17,9,10,20,32,50,23,41,6,9,48,11,58,12,8,3,
36,40
Range =L-S=58-2=56. No of classes=56/10=5.6
CLASS TALLY FREQUENCY
0-10 //// // 7
10-20
20-30
30-40
40-50
50-60

15. STEPS REQUIRED FOR THE CONVERSION OF
INCLUSIVE INTO EXCLUSIVE:
1. Find the difference between the lower limit of the second
class and the upper limit of the first class.
2. Divide the difference obtained in by two.
3. Subtract the values obtained in from lower limits of all
classes.
4. Add the value obtained in to upper limits of all classes.

16. CLASS F
0-4 1
5-9 2
10-14 3
15-19 4
20-24 5
CLASS F
0-4.5 1
4.5-9.5 2
9.5-14.5 3
14.5-19.5 4
19.5-24.5 5

17. Loss of information:
Statistical calculations are based only on the values of
class mark and not on the values of the observations in that
class. so other values of the class are not considered .It is
called loss of information

18. Frequency distribution with unequal classes
CLASS F
0-10 5
10-20 7
20-30 25
30-40 30
40-50 3
CLASS F
0-10 5
10-20 7
20-25 10
25-30 15
30-35 17
35-40 13
40-50 3

19. FREQUENCY ARRAY
For a discrete variable, the classification of its data is known
as a Frequency Array. Since a discrete variable takes values
and not intermediate fractional values between two integral
values, we have frequencies that correspond to each of its
integral values. SIZE OF HOUSEHOLD F
1 5
2 7
3 25
4 30
5 3

20. Prepare a frequency array from the following data
23,27,23,29,27,23,22,21,24,25,25,26,22,30,28,24,29,
30
ITEMS TALLY F
21 / 1
22 // 2
23
24
25
26
27
28
29
30

21. UNIVARIATE AND BIVARIATE FREQUENCY
DISTRIBUTION:
The frequency distribution of a single variable is called
univariate frequency distribution
A Bivariate Frequency Distribution can be defined as
the frequency distribution of two variables.