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Chapter 18: A. Basic Statistics and Applications 219
Continued
131 120 117 129 148 130 121 136 133 147
147 128 142 147 152 122 120 145 126 151
Prepare a frequency distribution table for these data.
Solution:
Following the steps described above, we have
1. Range (R) = 152 –110 = 42
2. Number of classes = 1 + 3.3 log 40 = 6.29, which, by rounding becomes 6
3. Class width = R/m = 42/6 = 7
The six classes we use to prepare the frequency distribution table are as follows:
110 – under 117, 117 – under 124, 124 – under 131,
131 – under 138, 138 – under 145, 145 – 152.
Note that in the case of quantitative data, each class is defined by two numbers. The
smaller of the two numbers is usually called the lower limit and the larger is called
the upper limit. Also, note that except for the last class the upper limit does not belong
to the class. This means, for example, that the data point 117 will be assigned to class
two and not class one. This way no two classes have any common point, which ensures
that each data point will belong to one and only one class. For simplification we will use
mathematical notations to denote the above classes as
[110 – 117), [117 – 124), [124 – 131), [131 – 138), [138 – 145), [145 –152]
where customarily the square bracket symbol “[“ implies that the beginning point
belongs to the class and the parenthesis “)” implies that the end point does not belong
to the class. The frequency distribution table for the data in this example is then as
shown in Table 18.4.
Table 18.4 Frequency table for the data on rod lengths.
Category Relative Cumulative
no. Tally Frequency frequency Percentage frequency
Part IV.A.4
[110–117) /// 3 3/40 7.5 3
[117–124) ///// // 7 7/40 17.5 10
[124–131) ///// /// 8 8/40 20.0 18
[131–138) ///// // 7 7/40 17.5 25
[138–145) ///// / 6 6/40 15.0 31
[145–152] ///// //// 9 9/40 22.5 40
Total 40 1 100%
Having discussed the frequency distribution table we are now ready to study various
graphical displays of a data set.