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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
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