Biostatistics Graphical for grouped data

1. Graphical Distribution of
Grouped Data
BY
Dr. Aswartha Harinatha Reddy
Department of Life Sciences
ANDHRA Pradesh

2. Histogram
• A histogram is an accurate graphical representation of the
distribution of numerical data or continuous set of data.
• It was first introduced by Karl Pearson.
• It is a kind of bar graph.
• Notice that, unlike a bar chart, there are no "gaps" between
the bars.
• Because a histogram represents a continuous data set, and as
such, there are no gaps in the data

3. • To construct a histogram from a ungrouped data you first
need to split the data into intervals, then count how many
values fall into each interval.
• Example: by using ungroup data
8,6,12,16,18,19,21,22,25,26,27,28.
Class intervals Tally age Frequency
1-10 II 2
11-20 IIII 4
21-30 IIIII 5

4. Histogram for grouped data:
Example: Draw Histogram for following data
Age No of patients
20-30 2
30-40 4
40-50 4
50-60 5
60-70 3
70-80 1
80-90 0
90-100 1

5. Frequency Polygons:
• A Frequency polygons is an accurate graphical representation
of the distribution of numerical data or continuous set of data or
grouped data.
• It is like that of Histogram but line segment used to represent
individual frequency rather than bar.
• Frequency polygons are also a good choice for displaying
cumulative frequency distributions.

6. To draw frequency polygons follow the following
steps:
• Choose the class interval, Mark the mid value of each interval
on the horizontal axes.
• Mark the frequency of the class on the vertical axes.
• Corresponding to the frequency of each class interval, mark a
point at the height in the middle of the class interval.
• Connect these points using line segment.
• The obtained representation is a frequency polygon.

7. Example 1: In a batch of 400 students, the height of students is
given in the following table. Represent it through a frequency
polygon.
Middle vlaue
130
140
150
160

8. Frequency polygons

9. Frequency curve:
• Frequency Curve is a smooth curve which corresponds to the
limiting case of a histogram computed for a frequency
distribution of a continuous distribution as the number of data
points becomes very large.

11. Ogive:
• Ogives also known as Cumulative histograms, are graphs
that can be used to determine how many data values lie above
or below a particular value in a data set.
• The cumulative frequency is calculated from a frequency table,
by adding each frequency to the total of the frequencies of all
data values before it in the data set.

12. Draw more than Ogive for the following data on the number
of HIV patients.
Age HIV Patients or Frequency Cumulative frequency
10-20 5 0+5=5
20-30 7 5+7=12
30-40 12 12+12=24
40-50 10 24+10=34
50-60 6 34+6=40
Total frequency f=40 Total Cumulative frequency CF=40
The final cumulative frequency is always equal to the sum of all the frequencies.

13. • To draw Ogive follow the following steps:
• The first coordinate in the plot always starts at a y value of 0
because we always start from a count of zero.
• So, the first coordinate is at (10;0) at the beginning of the first
interval.
• The second coordinate is at the end of the first interval (which is
also the beginning of the second interval) and at the first cumulative
count, so (20;5).
• The third coordinate is at the end of the second interval and at the
second cumulative count, namely (30;12) and so on.

14. • Ogive do look similar to frequency polygons, which we saw earlier.
• The most important difference between them is that an ogive is a
plot of cumulative values, whereas a frequency polygon is a plot of
the values themselves.

15. Thank you