calledleaves. There are no hard rules about how to construct a stem-and-leaf
diagram. Generally, it consists of the following steps:
- Choose some convenient/conventional numbers to serve as stems. The
stems chosen are usually the first one or two digits of individual data
points. - Reproduce the data graphically by recording the digit or digits following
the stems as a leaf on the appropriate stem.
If the final graph is turned on its side, it looks similar to a histogram (Figure
2.10). The device is not practical for use with larger data sets because some
stems are too long.
2.2 NUMERICAL METHODS
Although tables and graphs serve useful purposes, there are many situations
that require other types of data summarization. What we need in many appli-
cations is the ability to summarize data by means of just a few numerical mea-
sures, particularly before inferences or generalizations are drawn from the data.
Measures for describing the location (or typical value) of a set of measurements
and their variation or dispersion are used for these purposes.
First, let us suppose that we havenmeasurements in a data set; for example,
here is a data set:
f 8 ; 2 ; 3 ; 5 gwithn¼4. We usually denote these numbers asxi’s; thus we have for the
example above:x 1 ¼8,x 2 ¼2,x 3 ¼3, andx 4 ¼5. If we add all thexi’s in the
data set above, we obtain 18 as the sum. This addition process is recorded as
X
x¼ 18where the Greek letterSis the summation sign. With the summation notation,
Figure 2.10 Typical stem-and-leaf diagram.72 DESCRIPTIVE METHODS FOR CONTINUOUS DATA