PRESENTATION OF STATISTICAL DATA 535J
Figure 54.8
Therangeof the data is the member having the
largest value minus the member having the smallest
value. Inspection of the set of data shows that:
range= 9. 1 − 7. 1 = 2. 0The size of each class is given approximately byrange
number of classes.Since about seven classes are required, the size
of each class is 2.0/7, that is approximately 0.3, and
thus theclass limitsare selected as 7.1 to 7.3, 7.4 to
7.6, 7.7 to 7.9, and so on.
Theclass mid-pointfor the 7.1 to 7.3 class is
7. 35 + 7. 05
2
, i.e. 7.2, for the 7.4 to 7.6 class is
7. 65 + 7. 35
2, i.e. 7.5, and so on.
To assist with accurately determining the num-
ber in each class, atally diagramis produced as
shown in Table 54.4. This is obtained by listing the
classes in the left-hand column and then inspecting
each of the 50 members of the set of data in turn and
allocating it to the appropriate class by putting a ‘1’
in the appropriate row. Each fifth ‘1’ allocated to a
particular row is marked as an oblique line to help
with final counting.
Afrequency distributionfor the data is shown
in Table 54.5 and lists classes and their correspond-
ing frequencies. Class mid-points are also shown in
this table, since they are used when constructing the
frequency polygon and histogram.
Afrequency polygon is shown in Fig. 54.9,
the co-ordinates corresponding to the class mid-
point/frequency values, given in Table 54.5. The
co-ordinates are joined by straight lines and the poly-
gon is ‘anchored-down’ at each end by joining to the
next class mid-point value and zero frequency.
Ahistogramis shown in Fig. 54.10, the width of
a rectangle corresponding to (upper class boundary
value—lower class boundary value) and height cor-
responding to the class frequency. The easiest way to
Table 54.4Table 54.5Class Class mid-point Frequency7.1 to 7.3 7.2 3
7.4 to 7.6 7.5 5
7.5 to 7.9 7.8 9
8.0 to 8.2 8.1 14
8.1 to 8.5 8.4 11
8.2 to 8.8 8.7 6
8.9 to 9.1 9.0 2Figure 54.9Figure 54.10