A) Tabulation: Frequency distribution Table : - Quantitative - Qualitative B) Drawing: (Graphs / Charts/ Diagrams) Quantitative Data : i) Histogram ii) Frequency Polygon

iii) Frequency Curve iv) Line chart /graph v) Cumulative Frequency Diagram / Ogive vi) Scatter or Dot diagram vii) Stem & Leaf plot Qualitative Data : i) Bar diagram (Simple / Multiple / Proportional) ii) Pie or Sector chart iii) Pictogram

General principles in designing table:

The tables should be numbered e.g., Table-1, Table-2 etc.

There should be a brief and self-explanatory title, mentioning time, place & persons.

The headings of columns and rows should be clear and concise

The data must be presented according to size or importance; chronologically, alphabetically or geographically

Data must be presented meaningfully

No table should be too large

Foot notes may be given, if necessary

Total number of observations (n) i.e the denominator should be written

The information obtained in the table should be summarized beneath the table

Characteristics Population (in million) %

MaleFemale

7.076.14

53.5246.48

Total 13.21 100.00

TABLE-1 Population by sex in Kolkata urban area in 2001

Source: Health on the March 2004-05, Govt. of West Bengal

Frequency distribution table for qualitative data

Characteristics Population (in million) %

Male 7.07 53.52

Female 6.14 46.48

Total 13.21 100.00

Frequency distribution table for quantitative data

Pulse rate/minute No of medical students

Percentage

51-60 2 1.33

61-70 22 14.67

71-80 56 37.33

81-90 55 36.67

91-100 14 9.33

101-110 1 0.67

Total 150 100.00

Frequency Table

lists classes (or categories) of values, along with frequencies (or counts)

of the number of values that fall into each class

2-2 Summarizing Data With Frequency Tables

Rating of length measurement Table

2 2 5 1 2 6 3 3 4 2

4 0 5 7 7 5 6 6 8 10

7 2 2 10 5 8 2 5 4 2

6 2 6 1 7 2 7 2 3 8

1 5 2 5 2 14 2 2 6 3

1 7

Frequency Table of rating of length

Table 2-3

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

rating Frequency

Frequency Table

Definitions

Lower Class Limits are the smallest numbers that can actually belong

to different classes

Lower Class Limits are the smallest numbers that can actually belong

to different classes

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

rating Frequency

Lower Class Limits are the smallest numbers that can actually belong

to different classes

Lower ClassLimits

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

rating Frequency

Upper Class Limits are the largest numbers that can actually

belong to different classes

Upper Class Limits are the largest numbers that can actually

belong to different classes

Upper ClassLimits

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

rating Frequency

are the numbers used to separate classes, but without the gaps created by class limits

Class Boundaries

number separating classes

Class Boundaries

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Rating Frequency

- 0.5 2.5

5.58.5

11.5

14.5

Class Boundaries

ClassBoundaries

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Rating Frequency

-0.5

2.5

5.58.5

11.5

14.5

number separating classes

midpoints of the classes

Class Midpoints

midpoints of the classes

Class Midpoints

ClassMidpoints

0 - 1 2 20

3 - 4 5 14

6 - 7 8 15

9 - 10 11 2

12 - 13 14 1

Rating Frequency

is the difference between two consecutive lower class limits or two consecutive class boundaries

Class Width

Class Width

Class Width

3 0 - 2 20

3 3 - 5 14

3 6 - 8 15

3 9 - 11 2

3 12 - 14 1

Rating Frequency

is the difference between two consecutive lower class limits or two consecutive class boundaries

Relative Frequency Table

relative frequency =class frequency

sum of all frequencies

Relative Frequency Table

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Rating Frequency

0 - 2 38.5%

3 - 5 26.9%

6 - 8 28.8%

9 - 11 3.8%

12 - 14 1.9%

RatingRelativeFrequency

20/52 = 38.5%

14/52 = 26.9%

etc.

Table 2-5Total frequency = 52

Cumulative Frequency Table

CumulativeFrequencies

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Rating Frequency

Less than 3 20

Less than 6 34

Less than 9 49

Less than 12 51

Less than 15 52

RatingCumulativeFrequency

Table 2-6

Frequency Tables

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Rating Frequency

0 - 2 38.5%

3 - 5 26.9%

6 - 8 28.8%

9 - 11 3.8%

12 - 14 1.9%

RatingRelativeFrequency

Less than 3 20

Less than 6 34

Less than 9 49

Less than 12 51

Less than 15 52

RatingCumulative Frequency

Table 2-6Table 2-5Table 2-3

Bar GraphThe widths of the bar should be equalThe bars are usually separated by appropriate

spaces with an eye to neatness and clear presentation. The spaces between two bars are usually kept equal to the width of the bars.

The length of the bar is proportional to the frequency.

A suitable scale must be chosen to present the length of the bars.

The Y-axis corresponds to the frequency in vertical bar diagram, whereas the X-axis corresponds to the frequency in a horizontal bar diagram

Simple Bar DiagramHIV+ve cases in six districts of West

Bengal in 2004

050

100150200250300350

Nadia 24Pgs(N)

24Pgs(S)

Howrah Hoogly Kolkata

Simple ar Diagrameach bar represents

frequency of a single

category with a

distinct gap from

another bar

..

Multiple / Compound Bar diagram

0

50

100

150

200

250

Nadia 24Pgs(N)

24Pgs(S)

Howrah Hoogly Kolkata

Male

Female

show the

comparison of

two or more

sets of related

statistical data

.

Component /Segmented Bar diagram

0500

1000150020002500300035004000

Ban Bar Bir Hao Hug Kol Nad 24 p(N)

24 P(S)

New smear +ve Pul. TB cases by sex in few districts of West Bengal in 2003

Female

Male

• to compare sizes of the different component parts among themselves

• also show the relation between each part and the whole.

PIE DiagramCauses of Maternal deaths of West Bengal in 2005

17%

16%

6%

27%

2%

5%

27%Anaemia

Haemorrhage

P. Sepsis

Toxaemia

Tetanus

Obstructed labour

Other cases

•For for qualitative or discrete data•Areas of sectors are proportional to frequencies •Angle (degree) of a sector=Class % X3.6,

• Expressing proportional components of the attributes

•compared with that of other segments as well as the whole circle.

HistogramA histogram is a bar graph that shows the frequency of each item. Histograms combine data into equal-sized intervals.

There are no spaces between the bars on the histogram.

Line GraphA line graph uses a series of line segments to

show changes in data over time.Plot a point for each data item, and then

connect the dots with straight line segments.

Refer to page 336 for the line graph.

Frequency Polygon - Frequency Distribution graph

- Joining mid-points of histogram blocks (class intervals)

- When no. of observations are very large: Frequency Polygon loses it’s angulations & giving a smooth curve: Frequency Curve

Frequency Distribution Haemoglobin Level

Frequency Polygon

-Frequency polygon presenting variations by time

- Trend of an event occurring over a time

Year

1901

1911

1921

1951

1961

1971

1941

1931

Line Chart or GraphGrowth rate in India from 1921-1931 to 1991-

2001

1114.22 13.31

21.51

24.8 24.66 23.85 22.66

0

5

10

15

20

25

30

1921-1931

1931-1941

1941-1951

1951-1961

1961-1971

1971-1981

1981-1991

1991-2001

Years

Gro

wth

rat

e

the trend of an event occurring over a period of time

Ogive (Cumulative frequency polygon

• to find the median,

quartiles, percentiles

Stem-and Leaf Plot

Raw Data (Test Grades)

67 72 85 75 89

89 88 90 99 100

Stem Leaves

6 7 8 910

72 55 8 9 90 9 0

Scatter Diagram

••

••

••

••

• •••

••

0

0.0 0.5

••

•••

•

1.0 1.5

10

20

•

NICOTINE

TAR

A plot of paired (x,y) data with the horizontal x-axis and the vertical y-axis. will discuss scatter plots again with the topic of correlation.Point out the relationship that exists between the nicotine and tar – asthe nicotine value increases, so does the value of tar.