Percentage’) freq.dist #R output
| Frequency | Cum.Frequency | Cum Percentage | |
| 1 | 28.00 | 28.00 | 25.45 |
| 2 | 26.00 | 54.00 | 49.09 |
| 3 | 20.00 | 74.00 | 67.27 |
| 4 | 16.00 | 90.00 | 81.82 |
| 5 | 20.00 | 110.00 | 100.00 |
Note that sometimes a quantitative data set is such that it consists of only a few distinct observations that occur repeatedly. These kind of data are usually summarized in the same manner as the categorical data. The categories are represented by the distinct observations. We illustrate this scenario with the following example.
Example 2.3.3 (Hospital data) The following data show the number of coronary artery bypass graft surgeries performed at a hospital in a 24‐hour period for each of the last 50 days. Bypass surgeries are usually performed when a patient has multiple blockages or when the left main coronary artery is blocked. Construct a frequency distribution table for these data.
| 1 | 2 | 1 | 5 | 4 | 2 | 3 | 1 | 5 | 4 | 3 | 4 | 6 | 2 | 3 | 3 | 2 | 2 | 3 | 5 | 2 | 5 | 3 | 4 | 3 |
| 1 | 3 | 2 | 2 | 4 | 2 | 6 | 1 | 2 | 6 | 6 | 1 | 4 | 5 | 4 | 1 | 4 | 2 | 1 | 2 | 5 | 2 | 2 | 4 | 3 |
Solution: In this example, the variable of interest is the number of bypass surgeries performed at a hospital in a period of 24 hours. Now, following the discussion in Example 2.3.1, we can see that the frequency distribution table for the data in this example is as shown in Table 2.3.3. Frequency distribution table defined by using a single numerical value is usually called a single‐valued frequency distribution table.
Table 2.3.3 Frequency distribution table for the hospital data.
| Frequency | Cumulative | Cumulative | |||
| Categories | Tally | or count | frequency | Percentage | percentage |
| 1 | ///// /// | 8 | 8 | 16.00 | 16.00 |
| 2 | ///// ///// //// | 14 | 22 | 28.00 | 44.00 |
| 3 | ///// //// | 9 | 31 | 18.00 | 62.00 |
| 4 | ///// //// | 9 | 40 | 18.00 | 80.00 |
| 5 | ///// / | 6 | 46 | 12.00 | 92.00 |
| 6 | //// | 4 | 50 | 8.00 | 100.00 |
| Total | 50 | 100.00 |
2.3.2 Quantitative Data
So far, we have discussed frequency distribution tables for qualitative data and quantitative data that can be treated as qualitative data. In this section, we discuss frequency distribution tables for quantitative data.
Let
1 Step 1. Find the range of the data that is defined as(2.3.1)
2 Step 2. Divide the data set into an appropriate number of classes. The classes are also sometimes called categories, cells, or bins. There are no hard and fast rules to determine the number of classes. As a rule, the number of classes, say , should be somewhere between 5 and 20. However, Sturges's formula is often used, given by(2.3.2) or
