(i) Quantitative classification: In quantitative classification the data are classified according to some characteristics that can be measured numerically such as height, weight, production, income, marks secured by the students etc.
Example: Students of a college may be classified according to there weights as given in the table

Weight (in Kg)	No of students
30-40 40-50 50-60 60-70	20 25 40 45

(ii) Qualitative classification: In qualitative classification the data are classified on the basis of attributes or quality such as sex, colour of hair, literacy, religion etc.

Following steps are followed to convert an exclusive series into an inclusive series.
(a) Find the difference between upper limit of preceding class and lower limit of succeeding class.
(b) Divide this difference by 2.
(c) Add this number in upper limit of all classes and deduct this number from lower limit of all classes.
For example, if classes are 0 - 9, 10 - 19, 20 29 and so on. Then the difference between upper limit and lower limit of two succeeding classes is one. When we divide it by 2, we get 0.5. Therefore on deducting this number from upper limit and adding this number in lower limit, we can get new class intervals as- (-) 0.5 - 9.5,9.5 - 19.5, 19.5 and so on.

When we group data in a continuous series as shown below, we get to know only the fact that 4 students have marks more than equal to or more than 0 and less than 10 but we do not know the exact figures.

Marks	Frequency
0-10	4
10-20	7
20-30	4
30-40	3
40-50	2

Suppose all 4 had 1 mark, they will be in class 0-10 and even when all 4 have 9 marks, they will be in class 0-10. It is called loss of information in organized data.

Cumulative Frequency series is one in which the frequencies are continuously added corresponding to each class interval of the series. It can be prepared from discrete frequency distribution as well as continuous frequency distribution. It can be of two types:
(a) Cumulative Frequency Series of less than type: It is prepared on the basis of upper limit and show how many items lie below some value.
(b) Cumulative Frequencies of more than type: These are prepared on the basis of lower limit of the classes and shows how many items lie above a given value.
Let us take an example to understand how a simple series is converted into cumulative frequency series.
Suppose we know the marks distribution of 50 students in the form of a simple continuous frequency distribution.

Marks	Frequency
0-10	4
10-20	7
20-30	4
30-40	3
40-50	2

 Cumulative frequency series of less than type

Marks	Frequency
Less than 10	4
Less than 20	4+7=11
Less than 30	11+4 = 15
Less than 40	15+3 = 18
Less than 50	18+2 =20

Cumulative frequency series of more than type

Marks	Frequency
More than 10	20
More than 20	20-4= 16
More than 30	16-7=9
More than 40	9-4=5
More than 50	5-3=2

As frequencies shown in different types of series discussed so far were absolute frequencies. These were shown in absolute numbers. Sometimes, it is important to know the relative importance of each class. Therefore, frequencies are shown in percentage of total observations. An example is given below:

Marks	Absolute Frequency	Relative Frequency(%)
0-10	4	20
10-20	7	35
20-30	4	20
30-40	3	15
40-50	2	10
Total	20	100

Spatial Classification: In spatial classification, data are classified according to geographical areas.
Example: Statewise classification of production of food grains in India:

State	Production of food grains (in tons)
Orissa A.P U.P Assam	3,00,000 2,50,000 22,00,000 1,00,00,000

Chronological classification:
In this type of classification the data are classified according to different time periods.
Example: Population of India for different time periods.
Profits of a business establishment over different years.

Year	Population (in crores)
1921 1931 1941 1951	24.8 27.3 31.8 35.6

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. To be meaningful, classification should have following characteristics.
(a) It should be unambiguous: Classification aims at removing ambiguity. It is a must that all classes should be defined in such a way that there is no room for doubt and confusion and each item must fit to at least and at most one class.
(b) The classes must not overlap: None of the item should be eligible to be a part of more than one class.
(c) It should be stable: Without stability, classified data will not be fit for comparison.
(d) Classification should be according to purpose of enquiry: For example, if I need to classify my students into two groups for bus arrangement, it will be better to use geographical classification. If the purpose is judging their academic performance the quantitative classification is more suitable. If purpose is judging their value system then qualitative classification is recommended.
(e) It should be mathematically accurate: The test of mathematical accuracy is confirmation of total items in the series with total items in the universe.
(f) It should be flexible: It should be flexible. It should be possible to adjust the series to new situations and circumstances. With change in time some figures may become obsolete and other may become more relevant.

(i) Range = Largest Value - Smallest Value
= 5090-1007= 4083
(ii)

Class Interval	Frequency	More than CF
1000-2000	33	50
2000-3000	11	17
3000-4000	3	6
4000-5000	2	3
5000-6000	1	1

(iii) (a) 33
(b) 6
(c) 19

Mid Value	Frequency	Classes
2	3	1-3
4	2	3-5
6	6	5-7
8	4	7-9
10	3	9-11