PRESENTATION OF DATA

• TEXTUAL• TABULAR•GRAPHIC

FUNCTIONAL PARTS OF TABLE

TABLE NUMBERTITLEHEAD NOTESTUB (RAW HEAD)BOX HEADBODT OR FIELDFOOT NOTE SOURCE NOTE

SIGNIFICANCE OF GRAPHS

• ATTRACTIVE PRESENTATION• SIMPLIFY COMPLEXITY• READILY INTELLIGIBLE• FACILITATE COMPARISON• SAVE TIME• HAVE GREAT MEMORISING EFFECT• CAN LOCATE MEDIAN MODE Etc.

LIMITATIONS

• ONLY APPROXIMATE PICTURE OF DATA• ONLY FOR COMPARATIVE STUDIES• CAPABLE OF BEING MISUSED EASILY• LIMITED AMOUNT OF INFORMATION• MEAN ONLY FOR LAYMAN

SIMPLE BAR DIAGRAM

INDIA GER U.K

CHINA

NEWZE

...

SWEDAN

05

1015202530354045 BIRTH RATE

BIRTH RATE

SUB DIVIDED BAR DIAGRAM

1996-97 1997-98 1998-990

10000

20000

30000

40000

50000

60000

SCIENCECOMMERCEARTS

MULTIPLE BAR DIAGRAM

1997 1998 1999 20000

20

40

60

80

100

120

140

160

SALESGROSS PROFITNET PROFIT

PERCENTAGE BAR DIAGRAM

2000 20010%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

PROFIT /LOSSMATERIALSPAINTINGWAGES

PIE DIAGRAMITEMS EXPENDITURE ITEMS EXPENDITURE

CEMENT 20% TIMBER 15%

STEEL 18% LABOUR 25%

BRICKS 10% MISCELLANEOUS 12%

CEMENT 20X3.6 72

STEEL 18X3.6 64.8

BRICKS 10X3.6 36

TIMBER 15X3.6 54

LABOUR 25X3.6 90

MISCELLANEOUS 12X3.6 43

PIE CHART

Sales

LABOURCEMENTSTEELTIMBERMISCELLANEOUSBRICKS

PICTOGRAMS

PICTOGRAMS ARE PICTORIAL REPRESENTATION OF

STATISTICAL DATA• ATTRACTS LAYMAN• DIFFICULT TO CONSTRUCT• NOT GIVE MINUTE DETAILS

CARTOGRAMS

CARTOGRAMS ARE STATISTICAL MAP PRESENTATION WHICH ARE

USED TO GIVE DATA OVER A GEOGRAPHICAL AREA.

• RAIN FALL IN INDIA• DENSITY OF POPULATION

HISTOGRAM

MARKS0

5

10

15

20

25

0-10Oct-2020-3030-4040-5050-6060-7070-8080-9090-100

FREQUENCY POLYGON

0 0-50 50-100 100-150 150-200 200-250 250-300 300-3500

5

10

15

20

25

30PROFIT/SHOP

PROFIT/SHOP

FREQUENCY CURVES

FREQUENCY CURVES ARE SMOOTH CURVED LINES OVER

FREQUENCY POLYGONAREA UNDER POLYGON AND

CURVE ARE SAME

OGIVES

• LESS THAN OGIVES • MORE THAN OGIVES

NO OF CHILDREN

0 1 2 3 4 5 6

NO OF FAMILIES

171 82 50 25 13 7 2

NO OF CHILDREN

LESS THAN 1

1LESS THAN

2

LESS THAN 3

LESS THAN 4

LESS THAN 5

5LESS THAN 6

6LESS THAN 7

NO OF FAMILIES

171 253 303 328 341 348 350

NO OF CHILDREN 0-1 1-2 2-3 3-4 4-5 5-6 6-7

NO OF FAMILIES 171 82 50 25 13 7 2

NO OF CHILDREN

0 OR MORE

1 OR MORE

2 OR MORE

3 OR MORE

4 OR MORE

5 OR MORE

6 OR MORE

NO OF FAMILIES

350 179 97 47 22 9 2

OGIVE BY LESS THAN METHOD

0 2 3 4 5 6 70

50

100

150

200

250

300

350

400 NO OF CHILDREN

NO OF CHILDREN

OGIVE BY MORE THAN

0 1 2 3 4 5 60

50

100

150

200

250

300

350

400

NO OF CHILDREN

NO OF CHILDREN

TIME SERIES GRAPH

1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 19870

50

100

150

200

250

EXPORTIMPORT

INDEX NUMBERS

• INDEX NUMBER MEASURE CHANGES IN A VARIABLE WITH RESPECT TO TIME

SIMPLE INDEX NUMBERS

• P01= INDEX NUMBER OF CURRENT YEAR• ∑P1 = TOTAL OF CURRENT YEAR PRICES• ∑P0 = TOTAL OF BASE YEAR PRICES

Construct index number for2000 on the base of 1991 commodities unit 1999 price 2000 price

Wheat Quintal 200 250

Rice Quintal 300 400

Pulses Quintal 400 500

Milk Liter 2 3

clothing meter 3 5

commodities unit 1999 price(p 0) 2000 price(p1)

Wheat Quintal 200 250

Rice Quintal 300 400

Pulses Quintal 400 500

Milk Liter 2 3

clothing meter 3 5

∑P0=905 ∑P0=1158

price in 2000 were 27.96% higher than 1999 price

commodities unit 1999 price(p 0) 2000 price(p1)

Wheat Quintal 200 250

Rice Quintal 300 400

Pulses Quintal 400 500

Milk Liter 2 3

clothing meter 3 5∑P0=905 ∑P1=1158

Construct index number for1980 on the base of 1979

commodity Price 1979 Price 1980

fish 90 95

pulses 40 60

Packed basmathi 90 110

Special wheat 30 35

commodity Price 1979 Price 1980

fish 90 95

pulses 40 60

Packed basmathi 90 110

Special wheat 30 35

∑P0= 250 ∑P1 =300

• Price increased 20% in the year 1990 than 1989

Weighted index number(Laspeyers method)

• Here base year quantities(q0) are taken as weights

Construct weighted index number for1999 on the base of 1998

commodities 1998 (p0) Quantity(q0) 1999 (p1)

A 2 8 4

B 5 10 6

C 4 14 5

d 2 19 2

commodities

1998 (p0)

Quantity(q0)

1999 (p1)

p1q0 p0q0

A 2 8 4 32 16

B 5 10 6 60 50

C 4 14 5 70 56

d 2 19 2 38 38

∑p1q0=200 ∑p0q0=160

solution

commodity 1995 price (p0)

Quantity(q0)

1996 price (p1)

p1q0 p0q0

Biscuit 3 10 3.25 32.50 30

Sugar 15 20 20 400 300

coffee 25 2 23 46 50

∑p1q0=478.5 ∑P0q0=380

Construct weighted index number

commodity 1995 price (p0) Quantity(q0) 1996 price (p1)

Biscuit 3 10 3.25

Sugar 15 20 20

coffee 25 2 23

Measures of central tendencies

AverageAN AVERAGE VALUE IS A SINGLE VALUE THAT IS

USED TO REPRESENT ALL THE VALUES IN THE SERIES

TYPES OF AVERAGES• ARITHMETIC MEAN• MEDIAN• MODE

ARITHMETIC MEAN

•MEAN IS OBTAINED BY DEVIDING THE SUM OF GIVEN OBSERVATION BY THEIR NUMBER

INDIVIDUAL SERIES

• FIND MEANArithmetic mean =

= 17

STUDENT MARKS

1 15

2 20

3 25

4 19

5 12

6 11

7 13

8 17

9 18

10 20

N=10 ∑x=170

Discrete series

value Frequency(f) f.x

5 13 75

15 20 300

25 25 625

35 24 840

45 12 540

55 31 1705

65 71 4615

75 52 3900

N = 250 ∑fx=12600

CONTINUOUS FREQUENCY DISTRIBUTIONclass f Mid value fm

0-10 3 5 15

10-20 2 15 30

20-30 5 25 125

30-40 8 35 280

40-50 4 45 180

50-60 6 55 330

60-70 2 65 130

N = 30 ∑ fm = 1090

MEDIAN• MEDIAN IS THE MIDDLE MOST

OBSERVATION,AFTER THE OBSERVATION ARRANGED IN ASCENDING OR DECENDING ORDER OF THE MAGNITUDE

FIND MEDIAN? ASCENDING

4 4

45 11

60 12

20 19

83 20

19 2626 27

11 45

27 52

12 60

52 83

N = 11

MEDIAN-INDIVIDUAL SERIES N=11 (n is odd)MEDIAN =

FIND MEDIAN? ASCENDING

4 4

45 11

60 12

20 19

83 20

19 26

26 27

11 45

27 52

12 60

IF n IS EVEN median =

Median – discrete seriessize frequen

cyCumulative frequency

5 3 38 12 15

10 8 2315 7 3020 5 3525 4 39

N = 39

20th ITEM20th item lies in 23 cf the size of item is 10 or median is 10

CONTINUOUS SERIES - MEDIAN

L= lower limit of median classCf = cumulative frequency of class preceding median class.F = frequency of median classC = class interval of median class

Median class80/2=4040 lies in 140-160 class

MARKS NO OF STUDENTS

CUM FREQ

100-120 10 10

120-140 20 30

140-160 30 60

160-180 15 75

180-200 5 80

N =80

=140+6.67=146.67

MODE

• MODE IS THE MOST FREQUENT OBSERVATIONINDIVIDUAL SERIES-BY INSPECTION U CAN FIND11,12,11,13,10 MODE=11DISCRETE SERIES– ITEM WITH HIGH FREQUENCY

VALUE 12 HAS HIGH FREQENCY THEREFORE

MODE = 12

SIZE 5 8 10 12 20 25 50 40

FREQ 3 11 24 40 30 19 18 7

MODE- CONTINUOUS SERIES

• L1 = Lower limit of modal class• F1,f2 = frequ of classes just preceding and Succeeding modal classC = class interval of modal class

Compute modeclass frequency

0-5 20

5-10 24

10-15 25

15-20 28

20-25 30

25-30 26

30-35 24

35-40 10

40-45 8

Highest frequency is 30Modal class-20-25

20+2.4 =22.4

LOCATING MODE GRAPHICALLY

MARKS0

5

10

15

20

25

0-10Oct-2020-3030-4040-5050-6060-7070-8080-9090-100

mode

DISPERSION

• DISPERSION MEASURES THE EXTEND TO WHICH THE ITEM VARY FROM SOME CENTRAL VALUE• THEY ARE AVERAGES OF

DEVIATION TAKEN FROM AN AVERAGE

RANGE

• SIMPLEST MEASURE OF DISPERSION RANGE = L-S• L = LARGEST ITEM• S = SMALLEST ITEM COEFFICIENT OF RANGE=

YEAR PROFIT1985 401986 301987 801988 1001989 1151990 851991 2101992 230

RANGE =L-SL=230S = 30230-30=200COEFFICIENT OF RANGE=

COMPUTE RANGE AND COEFFICIENT OF RANGE

CORRELATION

• CORRELATION IS A NUMERICAL MEASURE OF ASSOCIATION BETWEEN TWO VARIABLES

TYPES• POSITIVE OR NEGATIVE CORRELATION• LENEAR AND NON LENEAR CORRELATION

X Y

100 700

200 1400

300 2100

400 2800

LINEAR THE RATIO=1:7

THANK YOU

GOD BLESS YOU