direction, it effectively becomes a histogram. With this technique some of the descriptive statistics
relating to the frequency distribution, such as the mean, the mode and the median, can easily be
ascertained; however, the procedure for their calculation is beyond the scope of this book. Stem-and-
leaf displays are also possible for frequencies running into three and four digits (hundreds and

thousands).
FIGURE 16.8
The stem-and-leaf display
The pie chart
The
pie chart
is another way of representing data graphically (
Figure 16.9
), this time as a circle.
There are 360 degrees in a circle, and so the full circle can be used to represent 100 per cent, or the
total population. The circle or pie is divided into sections in accordance with the magnitude of each
subcategory, and so each slice is in proportion to the size of each subcategory of a frequency
distribution. The proportions may be shown either as absolute numbers or as percentages. Manually,
pie charts are more difficult to draw than other types of graph because of the difficulty in measuring
the degrees of the pie/circle. They can be drawn for both qualitative data and variables measured on
a continuous scale but grouped into categories.
FIGURE 16.9
Two- and three-dimensional pie charts
The line diagram or trend curve
A set of data measured on a continuous interval or a ratio scale can be displayed using a line diagram
or
trend curve
. A trend line can be drawn for data pertaining to both a specific time (e.g. 1995,
1996, 1997) or a period (e.g. 1985–1989, 1990–1994, 1995–). If it relates to a period, the midpoint
of each interval at a height commensurate with each frequency – as in the case of a frequency polygon
– is marked as a dot. These dots are then connected with straight lines to examine trends in a
phenomenon. If the data pertains to exact time, a point is plotted at a height commensurate with the
frequency. These points are then connected with straight lines. A line diagram is a useful way of
visually conveying the changes when long-term trends in a phenomenon or situation need to be
studied, or the changes in the subcategory of a variable are measured on an interval or a ratio scale

(
Figure 16.10
). Trends plotted as a line diagram are more clearly visible than in a table. For
example, a line diagram would be useful for illustrating trends in birth or death rates and changes in
population size.
The area chart
For variables measured on an interval or a ratio scale, information about the subcategories of a
variable can also be presented in the form of an
area chart
. This is plotted in the same way as a line
diagram but with the area under each line shaded to highlight the total magnitude of the subcategory in
relation to other subcategories. For example,
Figure 16.11
shows the number of male and female
respondents by age.
FIGURE 16.10
The line diagram or trend curve

FIGURE 16.11
The area chart
The scattergram
When you want to show visually how one variable changes in relation to a change in the other
variable, a
scattergram
is extremely effective.

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