Differentiate between Individual, discrete and continuous series.

Individual Series	Discrete Series	Continuous Series
In individual series, there is only one frequency for each item.	In case of discrete series, there is frequency of more than one for each item.	In case of continuous series, there is frequency of more than one for each item.
Individual series has one column and that is of observations.	In discrete there are two columns one for frequency and second for variable. Variable is a number.	In continuous series also, there are two columns as in discrete series but variable is in the form of a class
Values are given after a definite break.	Values are given after a definite break.	Values are in the form of groups.

A characteristic or phenomenon which is capable of being measured and changes its value from time to time, place to place or situation to situation is called a variable. In other words, anything which is subject to change in value and can be measured is called a variable. Variable means "which varies". It may vary over time, person to person, place to place etc. for example,Income is a variable as it varies person to  person (different people earn different incomes), place to place (salaries vary in India and America) and over time (salaries in 1951 were different from salaries in 2001). Temperature is a variable. It changes over time and also place to place. Height is a variable as it varies person to person and over time.
There are two types of Variable:
Discrete and Continuous
Discrete Variable: A discrete variable is one which increases in jumps or incomplete numbers. For example, there can't be 2.4 workers in a factory. They can be 1, 2, 3, 4 and so on. Similarly, a factory can't have 4.8 or 2/7 machines. It will be incomplete numbers like 1,2,3,4, and soon. Such variable are called discrete variable. Some other examples of discrete variable are number of workers in a factory, number of machines purchased, number of children etc.
Continuous Variable: Those variables which can assume any value in a given range and which increase continuously and not in jumps are called continuous variable. For example, weight of a person can be 45.234 kg, it can take any value within a range. No one gains weight in jumps. It increases in continuity. Other examples are height, income etc.

Following steps are involved in construction of a discrete frequency distribution:
(a) Arrange the series in ascending or descending order: First of all, arrange the raw data in ascending or descending order.
(b) Make as many classes as many are values of variable: Place all values of the variable in the first column of the series beginning with the lowest and giving the highest.
(c) Determine Frequency of each value: To determine frequency of a class, count, how many times a value is repeating itself. For counting, also make a column of tally bars before frequency. A vertical line is put for each repetition and after for five four lines are intersected like this
(d) Place Frequencies:Count the bars. Write it in front of each class in frequency column.
(e) Check Mathematical Accuracy:Total the frequency column to verify if sum total of frequencies is equal to number of total observations. 

Generally, data are classified on the basis of the following four bases:
Geographical Classification:
In geographical classification, data are classified on the basis of geographical or locational differences - such as cities, districts, or villages - between various elements of the data set. The following is an example of a geographical distribution. (Figures are hypothetical)

States of India	Punjab	Haryana	J & K	Bihar	Orissa	M.P.
Poverty (%)	12	10	3.5	39	38	34

Chronological Classification:
When data are classified on the basis of time, the classification is known as chronological classification. Such classifications are also called time series because data are usually listed in chronological order starting with the earliest period. The following is an example of a Chronological distribution. (Figures are hypothetical)

Year	1951	1961	1971	1981	1991	2001
Poverty (%)	52	50	47	38	36	26

Another example can be:

Month	Family expenditure per member
January	2000
February	3000
March	1000
April	1200
May	2300
June	1400
July	1100
August	4300
September	900
October	1900
November	2100
December	3100

Qualitative Classification:
In qualitative classification, data are classified on the basis of descriptive characteristics or on the basis of attributes like sex, literacy, region, caste, or education, which cannot be quantified. This is done in two ways:
Simple classification:
In this type of classification, each class is subdivided into two sub-classes and only one attribute is studied, for example male and female; blind and not blind, educated and uneducated; and so on.
Manifold classification: In this type of classification, a class is subdivided into more than two subclasses which may be sub-divided further. An example is given below:

Quantitative Classification: In this classification, data are classified on the basis of characteristics which can be measured such as height, weight, income, expenditure, production, or sales. An example is given below:

Salary Per Month	No. of workers
0-10000	40
10,000-20,000	10
·20000-30000	13
30000-40000	8
40,000-50,000	12
50,000 and above	7

(a) number of students securing mark less than 10 is 3, frequency for the class 0-10 is 3 number of students securing marks less than 20 and those of securing less than 10 is 3 therefore, if we subtract the number of those who secured marks less than 10 then we get the number of those who secured marks between 10 to 20. Their number is 2 (5-3=2). In this way we get frequency for the class 10 -20. In the same way we can find out frequencies of other classes also

Marks obtained (class interval)	No of students
0-10	3=3-0
10-20	2=5-3
20-30	5 = 10-5
30-40	8 = 18-10
40-50	7=25 -18
50-60	5=30-25

The number of workers whose wages are more than Rs 10 is 50 and those wages are more than Rs 20 is 35. Therefore the difference between these numbers of workers is the number of those workers whose wages are 10 to 20. Similarly, we can calculate the numbers of workers for other classes also

Wages (class interval)	No. of workers
10-20	15 = 50-35
20-30	10 = 35-25
30-40	5 = 25-20
40-50	2 = 20-18
50-60	8 = 18-10
60 and above	10 = 10

Cumulative Frequency of Less than Type

Marks	Cumulative Frequency
Less than 10	6
Less than 20	6 + 15 = 21
Less than 30	21 + 20 =41
Less than 40	41 + 4=45
Less than 50	45+ 3=48
Less than 60	48+2=50

Cumulative frequency series of more than type

Marks	Cumulative Frequency
More than 0	50
More than10	5-6=44
More than 20	44 -15 = 29
More than 30	29 -20 = 9
More than 40	9-4=5
More than 50	5-3=2

The difference between upper limit and lower limit of two successive classes is1.
Divide one by two.
We get 0.5
Add 0.5 in upper limit of all classes and deduct it from lower limit of all classes. On doing so we get new class intervals as follows:

Age	No of Students
(X)	(f)
- 0.5 -9.5	3
9.5 -19.5	4
19.5 - 29.5	10
29.5 - 39.5	7
39.5 - 49.5	63