FREQUANCY DISTRIBUTION

• 8, 24, 18, 5, 6, 12, 4, 3, 3, 2, 3, 23, 9, 18, 16, 1, 2, 3, 5, 11, 13, 15, 9, 11, 11, 7, 10, 6, 5, 16, 20, 4, 3, 3, 3, 10, 3, 2, 1, 6, 9, 3, 7, 14, 8, 1, 4, 6, 4, 15, 22, 2, 1, 4, 7, 1, 12, 3, 23, 4, 19, 6, 2, 2, 4, 14, 2, 2, 21, 3, 2, 9, 3, 2, 1, 7, 19.

FREQUANCY DISTRIBUTION

Age Group Frequency

0-4 IIII IIII IIII IIII IIII IIII IIII

35

5-9 IIII IIII IIII III 18

10-14 IIII IIII I 11

15-19 IIII III 8

20-24 IIII I 6

GRAPHIC AND DIAGRAMATIC PRESENTATION

• Useful method for presentation of data

• Impact on imagination of people

• Diagrams are better retained in mind of human.

• More attractive,

• Comparison of data

BAR CHART

COLOUR CHOICE OF MEDICAL STUDENTS FOR SHIRT

0

20

40

60

80

100

120

140

White Blue Yellow Green Pink

COLOR

NO

. O

F S

TU

DE

NT

S

COLUMN CHARTS

COLOR CHOICE BY MEDICAL STUDENTS

0 20 40 60 80 100 120 140

White

Blue

Yellow

Green

Pink

CO

LO

R C

HO

ICE

NO. O FSTUDENTS

BAR CHART

POPULATION OF PAKISTAN

16.6 19.4 21.1 23.6 28.3 33.7 42.964.9

83.8

112122 130.58

159

020406080

100120140160180

YEAR

PO

PU

LA

TIO

N I

N M

ILL

ION

S

MULTIPLE BAR CHART

0

20

40

60

80

100

120

140

White Blue Yellow Green Pink

Male

Female

COMPONENT BAR CHART

COLOUR CHOICE OF SHIRT BY MEDICAL STUDENTS

020406080

100120140160180

White Blue Yellow Green Pink

COLOUR

NO

. O

F S

TU

DE

NT

D

Female

Male

Frequency Polygon:

• It is obtained by joining mid points of the histogram blocks

FREQUENCY POLYGON

COLOUR CHOICES

0

20

40

60

80

100

120

140

White Blue Yellow Green Pink

COLOUR

NO

. O

F S

TU

DE

NT

S

FREQUENCY POLYGON

tuberculin reaction measured in 206 pts.

0

10

20

30

40

50

60

8--10 10--12 12--14 14--16 16--18 18--20 20--22 22-24

reaction mm

no

. o

f p

erso

ns

HISTOGRAMPATIENTS ATTENDING SZMC/H ON MONDAY

0

10

20

30

40

50

60

70

80

90

0--4 5--9 10--14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70 AND

ABOVE

AGE GROUP

Histogram

• Consists of adjacent rectangles having bases along x-axis and areas proportional to the class frequencies

HISTOGRAMTuberculin reaction positivity

28

21

42

24

52

32

48

0

10

20

30

40

50

60

8--10 10--12 12--14 14--16 16--18 18--20 20-22 22-24

reaction size

no

. o

f p

atie

nts

HISTORIGRAM

• It is a graph of time series

• Arrangement of data by their time of occurrence

• Time is marked on X-axis

• Variable is marked on Y-axis

HISTORIGRAM

PRODUCTION OF CIGARETTES IN PAKISTAN

01000020000300004000050000

YEAR

Cig

are

tte

s(M

)

LINEAR DIAGRAMLINE DIAGRAM OF POPULATION OF PAKISTAN

0102030405060708090

1901 1911 1921 1931 1941 1951 1961 1971 1981

YEAR

PO

PU

LA

TIO

N I

N M

ILL

ION

S

LINE DIAGRAM

INCIDENCE OF MALARIA CASES

010203040

Year

1972

1973

1974

1975

1976

1977

1978

YEAR

NO

. OF

CA

SES(

MIL

LIO

NS)

.

WORLD

ASIA

AFRICA

HISTOGRAM

0

5

10

15

20

25

30

35

FREQUENCY

37--40

41-44

45-48

49-52

53-56

57-60

61-64

65-68

69-72

73-76

77-80

81-84

HISTOGRAMPATIENTS ATTENDING SZMC/H ON MONDAY

0

10

20

30

40

50

60

70

80

90

0--4 5--9 10--14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70 AND

ABOVE

AGE GROUP

HISTOGRAM

FREQUENCY

0

5

10

15

20

25

30

35

37--40 41-44 45-48 49-52 53-56 57-60 61-64 65-68 69-72 73-76 77-80 81-84

PIE CHART

PIE CHART OF POPULATION OF PAKISTAN

Y-1901

Y-1911

Y-1921

Y-1931

Y-1941

tuberculin reaction

24

52

42

48

12

814 6

8--10

10--12

12--14

14--16

16--18

18--20

20--22

22-24

RELATION B/W AGE AND WEIGHT

CORRELATION BETWEEN AGE AND WEIGHT

0

2

4

6

8

10

0 5 10 15WEIGHT(Kg)

AG

E IN

M

ON

THS

DIRECT RELATIONSHIP

AGE & HEIGHT RELATIONSHIP

0

20

40

60

80

0 5 10 15AGE IN MONTHS

HE

IGH

T IN

Cm

SCATTER DIAGRAM

01020304050607080

0 5 10 15

WEIGHT

HEIGHT

RELATIONSHIP OF AGE AND A DISEASE

INVERSE RELATIONSHIP B/W AGE & PEM

0

20

40

60

80

100

0 50 100% AGE OF DISEASE OCCURRENCE

AG

E I

N

YE

AR

S

ANALYSIS OF DATA

• When characteristic and frequency are both variable

• Calculation are:

• Averages

• Percentiles

• Standard deviation,

• Standard error

• Correlation and

• Regression coefficients.

NORMAL

• Normal is not the mean or a central value but the accepted range of variation on either side of mean or average.

–Normal BP is not the mean but is a range between 100and 140 (mean 120 ± 20).

• Chances of even higher or lower are there.

HISTOGRAMPATIENTS ATTENDING SZMC/H ON MONDAY

0

10

20

30

40

50

60

70

80

90

0--4 5--9 10--14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70 AND

ABOVE

AGE GROUP

FREQUENCY CURVE

• When no. of observations is very large and group interval is reduced, the frequency polygon tends to lose its angulations giving place to a smooth curve known as frequency curve.

• This provides a continuous graph that is obtained in normal distribution of individuals in a large sample or of means in populations.

Normal distribution

histogram of weights of students

3 6 1645

90

136

195220

195

136

90

4516 6 30

50

100

150

200

250

weights

no. o

f stu

dent

s

Average

• We can find a single value which will represent all the values of the distribution in a definite way. The value used for this purpose to represent the distribution is called average. Averages tends to lie in the center of a distribution, they are called measures of central tendency.

• It is difficult to learn anything by looking data which have not been properly arranged

• When data is arranged into a frequency distribution the information contained in the data understood.

• Features of data become clear when frequency distribution is represented by means of graph.

MEASURE OF CENTRAL TENDENCY“AVERAGE”

• What is the average or central value?

• How are the values dispersed around this value?

• Degree of scatter?• Is the distribution normal ( shape of

distribution)

AVERAGE• Average value of a characteristic is the one

central value around which all other observations are dispersed.

• 50% of observations lie above and• 50% of values lie below the central value.• It helps

• To find most of normal observations lie close to central value

• Few of the too large or too small values lie far away at ends

• To find which group is better off by comparing the average of one group with that of other.

AVERAGE

• A term that describes the center of a series.

• Average or measure of central position

–Mean

–Median

–Mode

Mean

• Most commonly used average. It is the value obtained by dividing the sum of the values by their number i.e., summarizing up of all observations and dividing total by no. of observations

MEAN

• It implies arithmetic average or arithmetic mean which is obtained by summing up all the observations and dividing by the total number of observations.e.g.

• ESRs of 7 patients are 7,5,4,6,4,5,9

• Mean =7+5+4+6+4+5+9 =40/7=5.71 7

MEAN

• Tuberculin reaction of 10 boys was measured. find the mean?

5, 3, 8, 7, 8, 7, 9, 10, 11, 12

• Mean=8mm

MEDIAN

• When all observations are arranged in either ascending or descending order, the middle observation is called as median. i.e. mid value of series.

• Median is a better indicator of central value when one or more of the lowest or highest observations are wide apart or not so evenly distributed.

MEDIAN

• 83, 75, 81, 79, 71, 95, 75, 77, 84, 79, 75, 71, 73, 91, 93.

• 71, 71, 73, 75, 75, 75, 77, 79, 79, 81, 83, 84, 91, 93, 95.

• Median = 79

MODE

• Most frequently occurring observation in a series I.e. the most common or most fashionable value.

• 85, 75, 81, 79, 71, 95, 75, 77, 75, 90, 71, 75, 79, 95, 75, 77, 84, 75, 81, 75.

MODE

• Most frequently occurring observation in a series I.e. the most common or most fashionable value.

• 85, 75, 81, 79, 71, 95, 75, 77, 75, 90, 71, 75, 79, 95, 75, 77, 84, 75, 81, 75.

• Mode = 75.

NORMAL DISTRIBUTION

• Normal curve• Smooth, Bell shaped, bilaterally symmetrical

curve• Total area is =1• Mean is 0• Standard deviation=1• Mean, median, mode coincide.• Area between X±1 SD=68.3%• X±2SD=95.5%• X±3SD=99.9%

Normal distribution

histogram of weights of students

3 6 1645

90

136

195220

195

136

90

4516 6 30

50

100

150

200

250

weights

no. o

f stu

dent

s

NORMAL DISTRIBUTION

ADMITTED PATIENTS IN SZH

2

5

9

12

9

5

20

5

10

15

0--9 10--19 20--29 30--39 40--49 50--59 60--69AGE GROUP

POSITIVELY SKEWED

AGE WISE Pts VISITING SZH

2

5

12

97

4

10

5

10

15

0--9 10--19 20--29 30--39 40--49 50--59 60--69

AGE GROUP

NEGATIVELY SKEWED

AGE WISE Pts VISITING SZH

1

4

79

12

5

20

5

10

15

0--9 10--19 20--29 30--39 40--49 50--59 60--69

AGE GROUP

VARIABILITY

• Biological data are variable• Two measurements in man are variable• Cure rate are not equal but variable• Height of students in same age group is not

same but variable• Height of students in one area is not same as

compared to other place but variable• Variability is essentially a normal character• It is a biological phenomenon.

TYPES OF VARIABILITY

• Biological variability

– That occurs within certain accepted biological limits. It occurs by chance.

– Individual variability

– Periodical variability

– Class, group or category variability

– Sampling variability or sampling error

REAL VARIABILITY

– When the difference between two readings or observations or values of classes or samples is more than the defined limits in the universe, it is said to be real variability. The cause is external factors. e.g. significant difference in cure rates may be due to a better drug but not due to a chance.

Experimental variability

• Errors or differences due to materials, methods, procedures employed in the study or defects in the techniques involved in the experiment.– Observer error– Instrumental error– Sampling error.