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METHODS OF DATA PRESENTATION

DR. VAIBHAV GUPTA

MPH 1st year Student

Dept. of community medicine

JSSMC

27/03/13

Moderated by: Mrs. Vidyalaxmi

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Types of Data

Types of

Data

Quantitative

Data

Qualitative

Data

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Types of Data

Quantitative data are measurements that are recorded on a naturally occurring numerical scale.

Exp. Height in cm. ,weight in kg. ,blood pressure (mm/Hg)Qualitative data are measurements that cannot be measured on a natural numerical scale; they can only be classified into one of a group of categories. Exp . Sex, tall or short, blood group

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Presentation of data

• Frequency distribution table

• Graphic&Diagrametic presentation

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Class Frequency, f

1 – 4 4

5 – 8 5

9 – 12 3

13 – 16 4

17 – 20 2

Frequency Distributions

A frequency distribution is a table that shows classes or intervals of data with a count of the number in each class. The frequency f means the number of times a certain value of variable is repeated.

Frequencies

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Class Frequency, f

1 – 4 4

5 – 8 5

9 – 12 3

13 – 16 4

17 – 20 2

Class width

The class width is the distance between lower (or upper) limits of consecutive classes.

The class width is 3.

4 – 1 = 38 – 5 = 3

12 – 9 = 313-16=3

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Guidelines1. Condense the data by classifying them in to groups or

classes called as class intervals..2. It is best to select class intervals of equal size.3. Find the class width 4. Find the class limits. You can use the minimum entry

as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class. Then find the upper class limits.

5. Make a tally mark for each data entry in the row of the appropriate class.

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CONT………..6. Count the tally marks to find the total frequency f for

each class.

7. Class limits are specially started either inclusive or exclusive manner.

8. Inclusive manner- 45-49;50-54;55-59….

9. Excusive manner-45-50;50-55;55-60….

10.Interval may be represented by midpoints of class interval.

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Constructing a Frequency Distribution

18 20 21 27 29 20

19 30 32 19 34 19

24 29 18 37 38 22

30 39 32 44 33 46

54 49 18 51 21 21

Example:

The following data represents the ages of 30 students in a statistics class. Construct a frequency distribution that has five classes.

Ages of Students

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Constructing a Frequency Distribution

Example continued:

250 – 57342 – 49434 – 41826 – 33

1318 – 25 Tally Frequency, fClass

30f

Number of

students

Ages

Check that the sum

equals the number in the sample.

Ages of Students

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Midpoint

The midpoint of a class is the sum of the lower and upper limits of the class divided by two. The midpoint is sometimes called the class mark.

Midpoint = (Lower class limit) + (Upper class limit)2

Frequency, fClass Midpoint41 – 4

Midpoint = 1

24 5

2 2.5

2.5

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Relative Frequency

ClassFrequency,

f

Relative Frequenc

y

1 – 4 4

The relative frequency of a class is the portion or percentage of the data that falls in that class. To find the relative frequency of a class, divide the frequency f by the sample size n.

Relative frequency = Class frequencySample size

Relative frequency 841

0.222

0.222

fn

18f fn

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Cumulative Frequency

The cumulative frequency of a class is the sum of the frequency for that class and all the previous classes.

3028252113

Total number of students

++++50 – 57 2

348

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42 – 4934 – 4126 – 3318 – 25

Frequency, fClass

30f

Cumulative Frequency

Ages of Students

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Graphical &Diagrammatic Presentation

• It provides a visual method of examining quantitative and qualitative data.

• It brings out clear and relative importance of different figures and helpful in finding out relation between two or more sets of data.

a. Presentation of qualitative data:

A. Bar diagrams

B. Line diagrams

C. Pie diagrams

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CONT………

D. Pictograms.

E. Map diagrams.

b. Presentation of quantitative data

A. Histogram

B. Frequency polygon

C. Cumulative frequency curve or ogive

D. Scattered diagram

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Presentation of qualitative data:(A)Bar diagram

(B)The Line diagram

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Example:

Figure (1) Crude birth rate of Gaza Strip . 1997-2001

(C)The Pie ChartCC

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Marital Status Frequency %Single 20 28

Married 30 41Divorced 10 14Widowed 12 17

Total 72 100

Distribution of a group of subjects by marital status

(D)Pictogram

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Fireflies

Day

s of

the

Wee

k

2020

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Presentation of quantitative data

1.The HistogramExamples:

Age in Years Number of patients

0 - 5 4

5 - 10 10

10 - 15 18

15 - 20 8

20 - 25 6

Total 46

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The Histogram

Examples:Number of patients

Age in Years

Distribution of a group of subjects by age

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2.The Frequency Polygon

• Examples:

Age in Years Sex Mid-point of interval

Males Females 20-30 3 2 (20+30)/2=25

30-40 5 5 (30+40)/2=35

40-50 7 8 (40+50)/2=45

50-60 4 3 (50+60)/2=55

60-70 2 4 (60+70)/2=65

Total 21 22

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The Frequency Polygon

• Example:

Figure (2): Distribution of a group of subjects by age and sex

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3.Cumulative Frequency Graph

A cumulative frequency graph or ogive, is a line graph that displays the cumulative frequency of each class at its upper class boundary.

17.5

Age (in years)

Ages of Students

24

18

12

6

30

0

Cum

ulati

ve fr

eque

ncy

(por

tion

of st

uden

ts)

25.5 33.5 41.5 49.5 57.5

The graph ends at the upper boundary of the last class.

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Class BoundariesExample:Find the class boundaries for the “Ages of Students” frequency distribution.

49.5 57.5

41.5 49.5

33.5 41.5

25.5 33.5

17.5 25.5The distance from the upper limit of the first class to the lower limit of the second class is 1.

Half this distance is 0.5.

Class Boundaries

50 – 57 2

3

4

8

13

42 – 49

34 – 41

26 – 33

18 – 25

Frequency, fClass

30f

Ages of Students

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4.The Scatter Diagram

• When two quantitative variables such as blood pressure and weight have been measured on the same set of individuals, a simple and effective way of describing them is the scatter diagram.

• Each individual’s X (first variable value) and y (2nd variable value) measurements are plotted as a point on the diagram.

• The X value plotted on the horizontal scale.• The Y value on the vertical scale.• For example for the data below, the first individual’s weight is 67 kg,

his blood pressure is 114 mmHg. • The marked point in the figure corresponds to this individual's weight

and blood pressure.

Weight (kg) 67 69 85 83 74 81 97 92 114

SBP (mmHg) 114 90 88 96 113 92 103 123 125

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The Scatter diagramWeight (kg) 67 69 85 83 74 81 97 92 114

SBP (mmHg) 114 90 88 96 113 92 103 123 125

Scatter diagram of weight and systolic blood pressure for a group of individuals

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Thank you