Collection and presentation of data

My task

• As a teacher I have a Purpose.• My purpose is to teach you and make sure you

do well in the exams• For this I need to know your level, your strength

and weakness• To understand this I will keep testing you.• Based on the results I get I will know how to help

you.

Test done results received

Sameeha Iyer 32

This is the marks of Sameeha.I cannot take any action based on this because I don’t know the marks of other students.So this is only a fact and not a data.To take any action I need DATA.

Data means quantitative information which is expressed as a total.For example – data about income, population, prices etc. Data is also called statistical data or statistics.

Data is the total of all students in the class.Marks of one student is only a Fact.

Test done results receivedSr. No Name Marks

1 Abdur Rahman 322 Aliarsh 183 Angad 454 Chinmay 335 Deepak H 186 Devinder Jeet 257 Dilona F 218 Eliza F 379 Hari Santosh 1610 Hari Shankar 1611 Heena Momin 2412 Hitendra D 2013 Manas Shah 2214 Mayur Shetty 1815 Megha R.P 2616 Nikita .V 3717 Omkar Patil 3718 Pooja Sharma 2619 Sameeha Iyer 3220 Shivam Rawat 1621 Shruti mugul 3422 Shruti P 2123 Tabish 1624 Tamana Mallick 3825 Taniya Yadav 4226 Tanvi Kokare 31

The characteristics of data are –

1) Statistics are aggregates of facts.2) They are expressed as numbers.3) Data can be affected by a number of causes.4) It does not give 100 % accuracy.5) Data is collected for a predetermined purpose.

Now I have the marks of all the students.

Importance of Data in economics ….

• In economic planning: To prepare a future plan we need the data of the previous year.

• If we need to plan the expenditure for education for a year we need data regarding number of students, expenditure incurred etc. Based on these data’s we can plan for the coming year.

• To determine National income : In order to know the state of our economy it is important to know the national income.

• To know the national income we need to get information on the total wages received by all workers, rent received , interest received and profits earned by the entrepreneur in the given year.

• Government policies : Statistical data are used by government to frame policies for economic development of the country. In India Census is carried out once in every 10 years. This provides the government data of the total population, number of literates, number of employed people, number of old people… Based on this the government makes its policies.

Types of Data

• 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.

• 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.

• Secondary Data may exist in the form of Published or unpublished form.

• Published form it can be got/obtained from– Reports in newspapers, periodicals, RBI.– trade associations– SEBI publication– Official publications– International bodies like UNO, World bank etc.• Unpublished form may exist as

⁻ Internal reports of the government⁻ Records maintained by institutes⁻ Reports prepared by students

Presentation of Data

• Data collected are in the form of raw material.• To make use of them they need to be arranged,

organised.• Classification and Tabulation are the basic tools

of presenting raw data.• Classification is a process of arranging data into

classes or groups.

Variables and Attributes

• 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.

Name MarksAbdur Rahman 32Aliarsh 18Angad 45Chinmay 33Deepak H 18Devinder Jeet 25Dilona F 21Eliza F 37Hari Santosh 16Hari Shankar 16Heena Momin 24Hitendra D 20Manas Shah 22Mayur Shetty 18Megha R.P 26Nikita .V 37Omkar Patil 37Pooja Sharma 26Sameeha Iyer 32Shivam Rawat 16Shruti mugul 34Shruti P 21Tabish 16Tamana Mallick 38Taniya Yadav 42Tanvi Kokare 31

Raw Data

Sr. No Name Marks3 Angad 45

25 Taniya Yadav 4224 Tamana 3816 Nikita .V 378 Eliza F 37

17 Omkar Patil 3721 Shruti mugul 344 Chinmay 331 Abdur Rahman 32

19 Sameeha Iyer 3226 Tanvi Kokare 3115 Megha R.P 2618 Pooja Sharma 266 Devinder Jeet 25

11 Heena Momin 2413 Manas Shah 227 Dilona F 21

22 Shruti P 2112 Hitendra D 202 Aliarsh 185 Deepak H 18

14 Mayur Shetty 189 Hari Santosh 16

10 Hari Shankar 1620 Shivam Rawat 1623 Tabish 16

Arranged descending orderindividual series.

Arranged Discrete series

MarksNo. of students

16 418 320 121 222 124 125 126 231 132 233 134 137 338 142 145 1

X F0 - 10 -

10 - 20 820 - 30 730- 40 940 - 50 2X = GroupsF = Frequency

Arranged Continuous series

Individual, Discrete and continuous Series

Tabulation

• Tabulation – Once data is collected and classified, it can be put into rows and columns.

• This Process is called tabulation.

Diagrammatic presentation

• Diagrammatic presentation – The geometrical version of data is diagrammatic presentation.

• Example – bar diagram is a one dimensional diagram.

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• 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 value which represents the entire data.

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

1 + 2 + 2 + 2 + 3 + 96 = 19/6 = 3.17

• Arithmetic means are used in situations such as working out cricket averages.

• Arithmetic means are used in calculating average incomes.

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 =

fx01740

120808578

∑f = 140 ∑fx = 420

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

= ∑fx/∑f

= 420/140 =3

Discrete Series : Shortcut Methodx= Number of children per familyf = Number of familiesA = 2N= 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)

-2

-1

0

1

2

3

4

fdx

-26

-17

0

40

40

51

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 ( no. of students)

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 = take 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 ( no. of students)

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 +L2/2Step 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

Continuous Series : Shortcut Method Without step deviation

= A + ∑fdx/ ∑f x c