Collection and Presentation of data

Information

• Major source of knowledge• Helps in making decisions• With development of Science and technology

the sources of information has increased.• Books, magazines, internet, mobile phones,

T.V, newspapers are all medium of providing information.

Meaning of Data

• Information is both qualitative and quantitative.

• In the study of economics quantitative information's are mostly used for analysis.

• Data means quantitative information which is expressed as a total.

• Data is useful for making decisions.• It is also called statistical data.

Features/ Characteristics of Data1. Statistics are aggregate of facts.

– A single fact cannot be considered as a data.– For e.g. : Suresh got 56 marks in economics.– This is only a fact not a data.– The table below gives details of 12 students in a class.– With the help of this we can compare the performance of the whole class.– This is an example of DATA.

Students Marks Students Marks

Aditya 95 Harish 35

Bala 90 Kavita 30

Chetna 75 Leena 85

Dinesh 65 Manoj 20

Farida 90 Ravi 90

Gowri 100 Satish 80

3. Data are affected by multiple causes.• Data are affected by many factors.• Example: rise in price can be due to rise in demand or fall in supply or rise

in taxes.

2. They are expressed as numbers.(a) When facts are given by counting or calculation, then it is called data.(b) Hence data is quantitative and not qualitative.

Features/ Characteristics of Data

4. Statistics does not give 100% accuracy.– If a doctor invents a medicine to control diabetes and after conducting

a research he states that 90% of the people responded well to the medicine.

– This medicine is then considered good.

5. Data is always collected for a predetermined purpose.

Features/ Characteristics of Data

Statistics important in Economics• In economics statistics is important –• 1) In economic planning.

– The data of the previous years are used to prepare plans for the future.

– Forecasting is done on the basis of economic planning.

• 2) In calculating national income.– In order to know the state of the economy it is important

to know the national income.

• 3) In making government policies.

• Statistical data are widely used by governments to frame policies for economic development of the country.

• On the basis of Data collected the government had to make policy to remove poverty and unemployment.

• The government introduced the National Employment Guarantee Scheme, by which the government guarantees an unemployed person at least 100 days of employment in a year.

Primary data and Secondary data.

• On the basis of source of collection data can be classified as :

• Primary Data: – Data which is collected for the first time for a

particular purpose is called Primary data.• Secondary Data:

– When we use data that has already been collected by others then it is called Secondary data.

Various methods of collecting primary data

• There are five methods of collecting primary data. They are –

• 1) Direct personal investigation.• 2) Indirect investigation.• 3) Through correspondents.• 4) By mailed questionnaire.• 5) Through schedules.

Sources of Secondary Data• Secondary data may exist in the form of published or

unpublished form.Published form:– Newspapers and RBI reports.– Trade association reports.– Financial data reported in annual reports.– Reports made and published by UNO, World Bank etc.– Reports made by SEBI.

Unpublished form:• Internal reports of government departments.• Records maintained by institutions.• Research reports prepared by students in universities.

variable and attribute.

• Variable • 1)When data can be classified in terms of time or

size, it is called variable.• 2) For example – height, eight, length, distance

etc.• Attribute• 1)Data which cannot be classified in terms of time

or size is called attribute.• 2)For example – beauty, bravery, intelligence etc.

Classification • The process of arranging raw data into classes

or groups to make it usable is called classification.

• Data can be classified in the following ways – • (i) Individual series• (ii) Discrete series• (iii) Continuous series

Individual series• In this series items are shown individually with

their corresponding value.

Raw Data - Data is collected in its original form.

Array -This data is then arranged in ascending or descending order.

Students Marks Students MarksGowri 100 Satish 80Aditya 95 Chetna 80Bala 35 Dinesh 65Farida 90 Harish 35Ravi 90 Kavita 35Leena 85 Manoj 20

Students Marks Students MarksGowri 100 Chetna 80Aditya 95 Dinesh 65Farida 90 Bala 35Ravi 90 Harish 35Leena 85 Kavita 35Satish 80 Manoj 20

Discrete Series

• This series shows variables with definite breaks with their frequencies.

Marks No. of Students

100 1

95 1

90 2

85 1

80 2

65 1

35 3

20 1

Continuous Series• This kind of series places data with corresponding group of variables.

Marks No. of Students

10-20 1

20-30 0

30-40 3

40-50 0

50-60 0

60-70 1

70-80 0

80-90 0

90-100 3

Tabulation

• Once data is collected and classified, it can be put into rows and columns. This process is called tabulation.

Diagrammatic presentation

• The geometrical version of data is diagrammatic presentation.

• Example – bar diagram is a one dimensional diagram.

Data in a diagrammatic form –One dimensional diagram – Bar Diagram

Year Birth Rate

1931-40 45

1941-50 35

1951-60 30

1961-70 28

1971-80 24

1981-90 201931-40 1941-50 1951-60 1961-70 1971-80 1981-90

05

101520253035404550

Birth Rate

Birth Rate

Year

Birt

hRati

o 24 242830

35

Data in the form of a graph

Year No. of students

2007 1000

2008 2500

2009 3800

2010 4500

2011 5200

Analysis of Data

• Analysis of Data

• After Data has been collected, classified, tabulated and presented, it is studied to reach a conclusion.

• This is called analysis of data.

Central tendency

• One of the main aims of statistical analysis is to get one single value that describes the whole data.

• This single value is called average or mean.• An average measures the tendency of data to

move in a particular direction. • The tendency of data to group around the

central value or valve is called central tendency.

Arithmetic Mean

• Arithmetic mean is one of the methods of calculating central tendency.• It is an average.• It is calculated to

reach a single valuewhich represents the entire data.

• Calculating an Average• For example (1, 2, 2, 2, 3, 9). The arithmetic mean is

1 + 2 + 2 + 2 + 3 + 9 = 19 = 3.176 6Arithmetic means are used in situations such as working out cricket averages.

Arithmetic means are used in calculating average incomes.

Functions and purpose of average

• To make a summary of the collected information.

• To make comparisons between two or more groups

• To reach a value that represents the entire data.

• To make future policy and programme.

Calculation of Arithmetic Mean Individual SeriesFirst method : Direct Method

No. of marks got by 10 students out of 30 x

= ∑x/N 43

∑x = sum total no. of observations 89

N = Total no. of students 1210

4+3+8+9+12+10+25+21+20 2510 10

= 12.2 2120

Calculation of Arithmetic mean for Individual Series:

No. of marks got by 10 students out of 30 (x)

4389

121025102120

1. Assume a Mean (A)

2. Let us say the assumed mean(A) is 12

3. Formula = A + ∑dx/N ( ∑dx= is total of dx; N is the total no. of students) dx= x-A ( in this case since A= 12 it is x-12)

Arithmetic mean = A + (Total of all dx i.e ∑dx divided by total no. of students)12 + 2/ 10 = 12 + 0.2 = 12.2

dx4 - 123 - 128 - 129 -12

12 -1210 -1225-1210-1221-1220 -12

∑dx

dx= x-12-8-9-4-30-213-298

∑dx 2

= A + ∑dx/N =

Calculation of Arithmetic mean for Individual Series: Shortcut Method

Discrete Series : Direct Method

Number of Children per family

x0123456

Number of families having x no. of children

f13172040201713

fx13 x 017 x 120 x 240 x 320 x417 x 513 x 6

∑fx =

fx0

1740

120808578

∑f = 140 420

∑f = Total of f ∑ fx = Total of fxArithmetic Mean =

= ∑fx/∑f

= 420/140 =3

(f multiplied with x)

Discrete Series : Shortcut Methodx= Number of children per familyf = Number of familiesA = 2(number assumed by us)N= Total number of families

x

0

1

2

3

4

5

6

f

13

17

20

40

20

17

13

∑f = 140

dx = (x-A) (A=2)

0 – 2 = -2

1 – 2 = -1

2 – 2 = 0

3 – 2 =1

4 – 2 =2

5 – 2 = 3

6 – 2 = 4

fdx

13 x -2 = -26

17 x -1 = -17

20 x 0 = 0

40 x 1 =40

20 x 2 = 40

17 x 3 =51

13 x 4 = 52

∑fdx= 140

= A +∑fdx/∑f

= 2 + 140/ 140

= 2+1

= 3

Arithmetic mean =

Continuous Series : Direct Method

x (Marks

0-10

10-20

20-30

30-40

40-50

50-60

60-70

 

Mid Value

L1+L2 /2

(0+10)/2 5

(10+20)/2 15

(20+30)/2 25

(30+40)/2 35

(40+50)/2 45

(50+60)/2 55

(60+70(/2 65

   

f

23

27

40

120

40

27

23

∑f = 300

fx

23 x5

27x 15

40x25

120x35

40 x 45

27 x 55

23 x65

∑fx =

Step 1 = Find the mid value for each class

= Lower class + upper class /2= L1 + L2 / 2

Step 2 = Multiply f with the mid value to get fx

Arithmetic mean =

= ∑fx/ ∑f = 35= 10500/ 300

115

405

1000

4200

1800

1485

1495

10500

Continuous Series : Shortcut Method Without step deviation

Marks

0-10

10-20

20-30

30-40

40-50

50-60

60-70

 

Mid Value

L1+L2 /2 (x)

0+10/2 5

10+20/2 15

20+30/2 25

30+40/2 35

40+50/2 45

50+60/2 55

60+70/2 65

   

f

23

27

40

120

40

27

23

∑f = 300

dx = x -A (A=25)  

5-25 = -20

15-25 = -10

25-25 = 0

35-25 = 10

45-25 = 20

55-25 = 30

65-25 = 40

   

fdx

23 x -20 = -460

10 x 27 = -270

0 x 40 = 0

10 x 120 = 1200

20 x 40 = 800

30 x 27 = 810

40 x 23 = 920

∑fdx = 3000

Step 1 = take the mid value for each class = Lower class + upper class /2= L1 +L2/2

Step 2 = Assume A = 25

Step 3= find dx = x -A

Step 4 = Multiply f x dx

Step 5 = find ∑f total of f

∑fdx = total of fdx

Step 6

Step 7 find arithmetic mean

= A + ∑fdx / ∑f = 25 + 3000 / 300= 35

Summary of the Formulae’s for calculating arithmetic mean ;

• Individual Series :Direct Method : (∑x)

(N )

Shortcut Method = A + • Discrete Series :

Direct Method = (∑fx) (∑f)

Shortcut Method = A + (∑fdx) (∑f)

Continuous Method :

Direct Method (∑fx) (∑f)

Shortcut Method A+ (∑fdx) (∑f)

Shortcut Method (with step deviation) A+ (∑fdx') x c

(∑f)

Thank You