Economics 4 Marks Question

The given table in the form of more than series is shown below.

Item	Frequency (f)
More than 10	86 (total)
More than 20	86-12=74
More than 30	74-13=61
More than 40	61-18=43
More than 50	43-13=30
More than 60	30-12=18
More than 70	18-9=9
More than 80	9-8=1

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

'Less than' cumulative series

Marks	c.f.
Less than 10	4
Less than 20	10
Less than 30	20

'More than' cumulative series

Marks	c.f.
More than 0	20
More than 10	16
More than 20	10

‘Loss of information’ is a major drawback of the classified data. The classification or grouping of raw data into classes makes it more concise and understandable. But simultaneously there exists loss of information. The calculations involved in the classified data or the continuous series are based on the class midpoints. The items in such series cannot be exactly measured and consequently, an individual observation loses its importance during the statistical calculations. Further, the statistical calculations are based on the values of the class marks, ignoring the exact observations of the data leading to the problem of loss of information.

The bivariate frequency array for the given data is shown below.

Qualitative classification can take the following two forms:

1. Simple Classification: If the data are classified into only two classes, such a classification is termed as simple or dichotomous classification. Male-female, employed-unemployed, educated-uneducated are the examples of dichotomy.

2. Manifold Classification: If in a classification, data involves more than one characteristic, it is called manifold classification. A qualitative classification is referred to as a manifold classification in each of the two cases explained below.

1. When the given population is classified into more than two classes with respect to a given attribute such as intelligence, beauty, etc.

2. When the given population is first classified into two classes and then each of these classes are further classified into two or more classes.

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 understand-able.
3. Organization of data is useful in Comparison.
4. It saves time effort and energy by simplifying data.

Differences between inclusive series and exclusive series are:

S.No.	Basic	Inclusive Series	Exclusive Series
1.	Meaning	In inclusive series, the upper class limit of one class does not become the lower class limit of the succeeding class.	In exclusive series, the upper class limit of one class becomes the lower class limit of the succeeding class.
2.	Inclusion of Values	This series includes the values corresponding to the lower class limit, upper class limit and the values falling in the range of these limits.	This series includes the values corresponding to lower class limit, but not to upper class limit. Values falling in the range of lower class limit and one less than the upper class limit are also included.
3.	Relevance in Statistical Computation	This series has no relevance for statistical computation.	This series has relevance for statistical computation.
4.	Example	Group Frequency 0-9 5 10-9 10	Group Frequency 0-10 5 10-20 10

Difference between Inclusive and Exclusive Series

S.No.	Basis	Inclusive Series	Exclusive Series
1.	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.
2.	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.
3.	Utility	It can be used only when value is in complete number.	It can be used even when value is in decimals or fractions.
4.	Counting	In inclusive series, counting is not possible without converting it into exclusive series.	Counting can be done in all cases in exclusive series.

As in the question marks of 25 students are given in the individual series. For converting individual series into frequency array, tally bar should be used. he frequency array of given data is shown below.

As in the question, wages of 50 workers are given in the form of individual series. For converting individual series into frequency distribution, tally bar should be used.
The exclusive frequency distribution of given data is shown below.

The simple frequency distribution table on the basis of equal class interval is shown below.

Marks	Frequency
0-5	7
5-10	13[20-7]
10-15	25[38-25]
15-20	30[55-25]
20-25	20
25-30	4 [5-1]
30-35	1
Total	100

Less than' cumulative series.

Marks	Cumulative Frequency (cf)
Less than 10	4
Less than 20	10
Less than 30	20

Array: 50, 52, 52, 53, 54, 55, 55, 55, 56, 57 58, 59, 60, 60, 60, 60, 61, 62, 62, 62, 63, 63, 63, 63, 64, 65, 66, 67, 67, 68, 70, 72, 76, 77, 77, 78, 78, 79, 79, 79, 82, 86, 87, 87, 88, 88, 90, 91, 92, 95.

Yes, there are advantages in classifying things.The following points highlight the advantages of classification:

1. Simplification: Classification facilitates the arrangement of data in a presentable form which appears to be brief and simple for analysis.
2. Effective: Classification enhances the usage of data as it brings out similarity within the diverse set of data. Thus, classification of things is more effective and saves time when searching for information from huge data.

For example: Books in your school library are classified according to subjects as English, Mathematics, Science, Social Studies, GK and general story books. This enables students to refer to the particular subject book for detailed study. Thus, it saves the student's valuable time and effort during the course of study.

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:

1. 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.
2. 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

1. Array: 115, 129, 135, 144, 159, 169, 172, 173, 184, 196, 205, 212, 220, 220, 223, 229, 234, 238, 238, 238, 241, 243, 245, 256, 265, 271, 278, 298, 310, 335.

1. Number of families having expenditure less than ₹ 250 = 13
2. Number of families having expenditure more than ₹ 300 = 2
3. Number of families having expenditure between ₹ 200 and ₹ 300 = 18.

A cumulative frequency distribution is that in which the frequencies are progressively totalled and aggregates are shown.It can be of two types:

1. 'Less Than' Cumulative Frequency Distribution In this frequency distribution, the frequencies of each class interval are added successively from top to bottom.

Following is an example of 'less than' cumulative frequency distribution:

Size of Items	Cumulative Frequency (CF)
Less than 10	6
Less than 20	15
Less than 30	28
Less than 40	35

2. 'More Than' Cumulative Frequency Distribution: In this frequency distribution, the cumulative frequencies of each class interval is obtained by finding the cumulative total of frequencies starting from the highest value to the lowest value of class.

Class Interval	Cumulative Frequency (CF)
More than 0	35
More than 10	28
More than 20	15
More than 30	6

1.  

2.  

Following steps are involved in construction of a discrete frequency distribution:

1. Arrange the series in ascending or descending order: First of all, arrange the raw data in ascending or descending order.
2. 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 to the highest.
3. 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.
4. Place Frequencies: Count the bars. Write it in front of each class in frequency column.
5. Check Mathematical Accuracy: Total the frequency column to verify if sum total of frequencies is equal to number of total observations.

Classification of data implies conversion of raw data into statistical series.
There are different methods of classification of data like.

1. Spatial classification: When the raw data is classified with reference to geographical locations such as countries, states, cities etc. is known as spatial classification.
2. Chronological classification: When the raw data can be grouped according to time, it is known as “chronological classification”. In such a classification data is classified either in ascending or in descending order w.r.t. time such as years, months, days etc.
3. Qualitative classification: When the raw data is classified on the basis of qualities or attributes of data such as honesty, beauty, intelligence etc., it is known as qualitative classification.
4. Quantitative classification: When the raw data is classified on the basis of quantitative measurement such as age, height, weight, sales etc., it is known as quantitative classification.

Class Interval	Frequency (F)
0-5-5.5	10
5.5-10.	15
10.5-15.5	20
15.5-20.5	25
20.5-25.5	30
Total	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	24.8
1931	27.3
1941	31.8
1951	35.6

1. 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	20
40-50	25
50-60	40
60-70	45

2. 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.

The exclusive class interval table of given form is shown below.

Exclusive Class Interval	Frequency (f)
0-99.5	2
99.5-199.5	4
199.5-299.5	5
299.5-399.5	6
399.5-499.5	3
499.5-599.5	5
Total	25

In this case as lower limit of first class is zero, hence 0.5 will not be subtracted from it.