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2.3.1 Qualitative Data
ОглавлениеA frequency distribution table for qualitative data consists of two or more categories along with the numbers of the data that belong to each category. The number of data belonging to any particular category is called the frequency or count of that category. We illustrate the construction of a frequency distribution table when the data are qualitative with the following example.
Example 2.3.1 (Industrial revenue) Consider a random sample of 110 small to midsize companies located in the midwestern region of the United States, and classify them according to their annual revenues (in millions of dollars). Then construct a frequency distribution table for the data obtained by this classification.
Solution: We classify the annual revenues into five categories as follows: Under 250, 250–under 500, 500–under 750, 750–under 1000, 1000 or more. Then the data collected can be represented as shown in Table 2.3.1, where we have used the labels for the above categories.
Table 2.3.1 Annual revenues of 110 small to midsize companies located in mid‐western 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 | 3 | 2 | 5 | 2 | 5 | 2 | 1 | 2 | 3 |
| 3 | 2 | 1 | 2 | 5 | 3 | 2 | 1 | 1 | 2 | 1 | 2 | 4 | 5 | 3 | 5 | 1 | 3 | 1 | 2 | 1 | 4 | 1 | 4 | 5 | 4 | 1 | 1 | 2 |
| 4 | 1 | 4 | 1 | 2 | 4 | 3 | 3 | 4 | 1 | 4 | 1 | 4 | 1 | 2 | 1 | 5 | 3 | 1 | 5 | 2 | 1 | 2 | 3 | 1 | 2 | 2 | 1 | 1 |
| 2 | 1 | 5 | 3 | 2 | 5 | 5 | 2 | 5 | 4 | 3 | 5 | 2 | 3 | 2 | 3 | 5 | 2 | 3 | 5 | 5 | 2 | 3 | 2 | 5 | 1 | 4 |
After tallying the data, we find that of the 110 companies, 28 belong in the first category, 26 in the second category, 20 in the third category, 16 in the fourth category, and 20 in the last category. Thus, a frequency distribution table for the data in Table 2.3.1 is as shown in Table 2.3.2.
Table 2.3.2 Frequency distribution for the data in Table 2.3.1.
| Frequency | Cumulative | Cumulative | |||
| Categories | Tally | or count | frequency | Percentage | percentage |
| 1 | ///// ///// ///// ///// ///// /// | 28 | 28 | 25.45 | 25.45 |
| 2 | ///// ///// ///// ///// ///// / | 26 | 54 | 23.64 | 49.09 |
| 3 | ///// ///// ///// ///// | 20 | 74 | 18.18 | 67.27 |
| 4 | ///// ///// ///// / | 16 | 90 | 14.55 | 81.82 |
| 5 | ///// ///// ///// ///// | 20 | 110 | 18.18 | 100.00 |
| Total | 110 | 100.00 |
Interestingly, we can put technology to work on data in Table 2.3.1 to produce Table 2.3.2.
Example 2.3.2 (Industrial revenue) Using MINITAB and R, construct a frequency distribution table for the data in Table 2.3.1.
