DESCRIPTIVE METHODS FOR QUANTITATIVE DATA

1. DESCRIPTIVE METHODS
FOR QUANTITATIVE DATA
Dr. Boniphace M.Idindili
(MD, MPH, PhD)

2. Data presentation methods
• Frequency distributions
• Graphs
• Shapes of distributions

3. Frequency distributions
• Frequency and relative frequency
• Cumulative frequency and cumulative
relative frequency

4. Number of children per woman
Count Frequency Relative Cumulative relative
frequency frequency
0 4 3.1 3.1
1 27 21.0 24.1
2 27 21.0 45.1
3 20 15.6 60.7
4 16 12.5 73.2
5 17 13.4 86.6
6 12 9.5 96.1
7 2 1.6 97.7
8 1 0.8 98.5
9 2 1.6 100
Total 128 100

5. Cumulative Frequency of Haemoglobin
Haemoglobin | Frequency Cumulative Cumulative
| frequency percentage
------------+----------------------------------------------
8- 8.9| 1 1 1.4
9- 9.9| 3 4 5.7
10-10.9| 14 18 25.7
11-11.9| 19 37 52.9
12-12.9| 14 51 72.9
13-13.9| 13 64 91.4
14-14.9| 5 69 98.6
15-15.9| 1 70 100.0
------------+---------------------------------------------
Total | 70
Cumulative
percentage of
women with HB
below 11 is
25.7%

6. Types of diagrams
• Histograms
• Cumulative frequency curve
• Scatter diagram
• Line diagram

7. Histogram
• a way of visualizing a frequency table
graphically to see
– most common values
– spread of data
• values of a variable or class intervals are
represented on the horizontal scale
• the vertical scale represents the frequency or
relative frequency at each value
• each bar centres at the mid point of the class
interval

8. Example: Distribution of number of
children per woman among 128 women
0 1 2 3 4 5 6 7 8 9
Number of children
0
5
10
15
20
25
30
Frequency

9. Example: Distribution of Haemoglobin among 70
women attending clinic
Hb Frequency Percentage
8 – 8.9 1 1.4
9.0 – 9.9 3 4.3
10.0 – 10.9 14 20.0
11.0 – 11.9 19 27.1
12.0 – 12.9 14 20.0
13.0 – 13.9 13 18.6
14.0 – 14.9 5 7.1
15.0 - 15.9 1 1.4
Total 70 100.0
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Haemoglobin
• Area of bars represent frequency
• Important to ensure every value accounted for
• Histogram gives a good representation of the distribution of the variable

10. Cumulative frequency curves
• the vertical axis displays cumulative
relative frequency
• the point is placed at the upper limit of the
interval

11. Cumulative Frequency of Haemoglobin
Median = 50%
Median HB = 12
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Haemoglobin
Not so easy to
see distribution
Easier to use for
different grouping
intervals
Avoid problems of
calculating heights
of bars for
equalising areas

12. Scatter diagram
• A scatter diagram is a graph used for examining
the relationship between two continuous
variables
• Diagram shows visually the shape and degree of
closeness of the relationship
• Each point on the diagram represents a pair of
values, one based on X-scale and the other
based on Y-scale

13. 80
100
120
140
160
180
200
220
20 30 40 50 60 70 80 90
SBP (mm Hg)
Age (years)
Age and systolic blood pressure (SBP) among 33
adult women

14. Line diagram
• These are often used to express the change
in some quantity over a period of time
0
50
100
150
200
250
300
350
400
450
500
1994 1995 1996 1997 1998 1999 2000 2001 2002
rate
per
100000
0-4
5--14
15-59
60+
Injury mortality rate in Hai District

15. Shapes of frequency distributions - 1
• 3 most common shapes
• All have high frequencies on the centre of the
distribution and low frequencies at the two
extremes
– called upper and lower tails of the distribution

16. Shapes of frequency distributions - 2
• Symmetrical (bell shaped)
• Asymmetrical or skewed
• Positively skewed (skewed to the right): upper tail
longer than lower tail
• Negatively skewed (skewed to the left): lower tail
longer than upper tail

17. Examples of symmetric distributions

18. Skewed to the right (positively skewed)

19. Skewed to the left (negatively skewed)