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216 Part IV: Quality Assurance
Continued
Solution:
We can classify the annual revenues into five categories as follows:
(Under 250, 250 – under 500, 500 – under 750,
750 – under 1000, 1000 or more)
The data collected can be represented as shown in Table 18.1.
After tallying the above data we find that of the 110 companies, 30 belong in the
first category, 25 in the second category, 20 in the third category, 15 in the fourth category,
and 20 in the last category. Thus, the frequency distribution table for the data is
as shown in Table 18.2.
Table 18.1
Annual revenues of 110 small to mid-size companies located in the
Midwestern region of the United States.
1 4 3 5 3 4 1 2 3 4 3 1 5 3 4 2 1 1 4 5 5 3 5 2 1 2 1 2 3 3 2 1 5 3 2 1 1
1 2 2 4 5 5 3 3 1 1 2 1 4 1 1 1 4 4 5 2 4 1 4 4 2 4 3 1 1 4 4 1 1 2 1 5 3
1 1 2 5 2 3 1 1 2 1 1 2 2 5 3 2 2 5 2 5 3 5 5 3 2 3 5 2 3 5 5 2 3 2 5.
Table 18.2
Complete frequency distribution table for the 110 small to mid-size companies
located in the Midwestern region of the United States.
Category Relative Cumulative
no. Tally Frequency frequency Percentage frequency
1 ///// ///// ///// 30 30/110 27.27 30
///// ///// /////
Part IV.A.4
2 ///// ///// ///// 25 25/110 22.73 55
///// /////
3 ///// ///// ///// 20 20/110 18.18 75
/////
4 ///// ///// ///// 15 15/110 13.64 90
5 ///// ///// ///// 20 20/110 18.64 110
/////
Total 110 1 100%
Note that sometimes a quantitative data set is such that it consists of only a
few distinct observations that occur repeatedly. This kind of data is normally
treated in the same way as the categorical data. The categories are represented by
the distinct observations. We illustrate this scenario with Example 18.16.
Interpretation of a Frequency Distribution Table. In Table 18.3 the entries in
row 2, for example, refer to category 2. Entries in row 2, column 1 indicate that the
number of bypass surgeries performed in 24 hours is two, column 2 counts