Kumar-2011-Research-Methodology_-A-Step-by-Step-Guide-for-Beginners

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Research Methodology
of the intervals, whereas the latter is drawn by joining the end points of the intervals because
cumulative frequencies interpret data in relation to the upper limit of an interval. As a cumulative
frequency distribution tells you the number of observations less than a given value and is
usually based upon grouped data, to interpret a frequency distribution the upper limit needs to
be taken.
The stem-and-leaf display
The stem-and-leaf display is an effective, quick and simple way of displaying a frequency
distribution (Figure 16.8). The stem-and-leaf diagram for a frequency distribution running
into two digits is plotted by displaying digits 0 to 9 on the left of the y-axis, representing the
tens of a frequency. The figures representing the units of a frequency (i.e. the right-hand figure
of a two-digit frequency) are displayed on the right of the y-axis. Note that the stem-and-leaf
display does not use grouped data but absolute frequencies. If the display is rotated 90 degrees
in an anti-clockwise 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).
1 89
2 0001112222223344555556667777788899
3 0011122233333344555566677777889
4 112223333444555566779
5 000113355667
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.