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.

Differentiate between inclusive and exclusive series

Basis	Inclusive Series	Exclusive Series
Definition	An inclusive series is one in which there is generally a difference between the upper limit of one class interval and the lower limit of the other class interval.	An exclusive series is one in which there is generally no difference between the upper limit of one class interval and the lower limit of the other class interval.
Treatment	In inclusive series, value of upper limit of a class is included in that class.	In exclusive series, value of upper limit of a class is not included in that class
Utility	It can be used only when value is incomplete number.	It can be used even when value is in decimals or fractions
Counting	In inclusive series, counting is not possible without converting it into exclusive series.	Counting can be done in all cases in exclusive series.

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. 

According to Horace Secrist, "A series as used statistically may be defined as things or attributes of things arranged according to some logical order." According to Prof. Connor, "If two variable quantities can be arranged side by side so that measurable difference in the one corresponds with measurable difference in the other, the result is said to form a statistical series."
On the Basis of Characteristics:
(a) Time Series:
When series of values of some variable which is represented according to successive points in time is called time series. In such a series, data are represented with reference to a time period which can be a year, week, month or day. An example is given below:
Production in a cloth mill

Year	2005	2006	2007	2008	2009	2010
Production(in 000 tonnes)	15	27	58	72	134	140

or
Rainfall in a week

DAY	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Rainfall in cm	15	27	17	14	54	64	10

(b) Spatial Series: A series of values of some variable which is represented according to area under investigation i.e. geographical division of the universe is called spatial series. An example is given below:
Production of wheat in different states of India in 2010

States	Punjab	Haryana	Maharashtra	U.P	Bihar	Orissa
Production (in 000 tonnes)	1500	2700	580	720	134	140

(c) Condition Series: A series of values of some variables which is represented according to condition which may be expressed in quantitative terms is called condition series. An example is given below:

	Grade
	A	B	C	Total
Boys	13	25	11	49
Girls	7	20	6	33
Total	20	45	17	82

To understand these terms we are taking two series for reference one is discrete frequency distribution and second is continuous frequency distribution.
Series-1 Discrete Frequency Distribution

Shoe Size	7	8	9	10	11	12
No of Students	8	12	20	10	6	4

Series-2 Continuous Frequency Distribution

Marks	0-10	10-20	20-30	30-40	40-50	50-60
No of Students	8	12	20	10	6	4

(a) Frequency: Frequency is the number of times a value repeats itself in the observations. For example when we have written 8 before 7 in series 1, it means 8 students have a shoe size of 7 number in raw data. 12 students have got 8 size, 20 got 9 size and so on. It is applicable to discrete frequency distribution.
(b) Class Frequency: Frequency of a class instead of specific observation is called class frequency. It shows how many items have a value in that class interval. For example, when we have written 10 in column of number of students in front of 30-40, it means 10 students have got marks equal to or more than 30 but less than 40.
(c) Class: It refers to decided group of magnitudes. For example, 0-10 in series 2. It may be 0-9, 10-19 or 4.5 - 8.5 and so on.
(d) Upper and Lower limits of the Class: Lower limit is the lower magnitude of the class and upper limit is the upper magnitude of class. For example in class 0-10, 10 is the lower limit and 10 is the upper limit.
(e) Total Frequency: It is the sum total of frequencies of all classes. It must be equal to total number of observations.
(f)Frequency Distribution: When observations are distributed over several values, it is termed as frequency distribution. For example, in above examples, I series is an example of discrete frequency distribution of shoe size of students. Series 2 is a continuous frequency distribution of marks obtained by students.
(g) Class Interval: Class Interval refers to the magnitude spread between the lower and upper class limit. In other words, it is span or width of the class. It can be obtained by deducting lower limit from upper limit. It is applicable to continuous series only. In series two, class interval is 10 (10-0=10) for first class and for other classes as well. But it is not necessary that all classes should have same class interval. Depending on the purpose, unequal class intervals for different classes can also be used. For example:

Pocket Expenses	Frequency
0-10	2
10-30	9
30-100	3
100-500	5
500-1000	4
1000-2000	2

(h) Mid Value: It is the average of lower limit and upper limit. It can be obtained by dividing the sum of lower limit and upper limit by 2. For example, in series 2 given above, we can find mid values as follows:

Daily Income	No of families	Mid Value
0-100	5	50
100-200	9	150
200-300	12	250
300-400	2	350
500 -600	2	450

(i) Discrete Series: A series which represents a discrete variable is called discrete series. For example, series -1 of shoe size is a discrete series.
(j) Continuous Series: A series which represents continuous variable is called a continuous series. For example, in series 2, the distribution of marks amongst students is a continuous series.

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 classification is an ordered set of related categories used to group data according to its similarities. It consists of codes and descriptors and allows survey responses to be put into meaningful categories in order to produce useful data. Its objectives are as follows:
1. Organized data are attractive and impressive.
2. These are simple and easily understandable.
3. Organization of data is useful in Comparison
4. It saves time effort and energy by simplifying data.

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