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,...
TRANSCRIPT
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.