2.2.1 Concepts involved in frequency tables
The following terms are frequently used in frequency distribution:
Class interval or class limit: the lowest and the highest value defined for a class or group are called class limits. The lowest value is called the lower-class limit and the highest value is called the upper-class limit of that class. In the example in Table 5, the lower-class limits are 7, 9, 11, 13, 15, and the upper limits are 8, 10, 12, 14, 16. The terms class and class interval are often used interchangeably, although the class interval is a symbol for the class.
Class boundaries: a class boundary is the number that is used to separate the two different classes. It is the midpoint between the upper limit of a class and the lower limit of the next class. Each class has both an upper and a lower limit boundary. The lower boundary of a class is calculated by subtracting half of the value of the interval from the lower-class limit, while the upper boundary of a class is calculated by adding half of the value of the interval to the upper-class limit.
Referring to the example from JC Electrics, its class boundaries are given in Table 5.
| Class intervals | Class boundaries |
|---|---|
| 7–8 | 6.5–8.5 |
| 9–10 | 8.5–10.5 |
| 11–12 | 10.5–12.5 |
| 13–14 | 12.5–14.5 |
| 15–16 | 14.5–16.5 |
Referring to Table 5, you can say that the lower limit of the first-class interval is 6.5, as all values between 6.5 and 7.5 are recorded as 7. Meanwhile, the upper-class limit of 8 is 8.5, as all values between 7.5 and 8.5 are recorded as 8. The real class limit of a class is called a class boundary. A class boundary is obtained by adding two successive class limits and dividing the sum by 2. The value so obtained is taken as the upper-class boundary for the previous class, and lower-class boundary for the next class.
Midpoint or class mark: this is the average of a class interval, and is obtained by dividing the sum of upper- and lower-class limits by 2. Thus, the class mark of the interval 7–8 is 7.5, as (7+8)/2=7.5.
The size or the width of a class interval: the size, or width, of a class interval is the difference between the lower- and upper-class boundaries and is also referred to as the class width, class size, or class length. If all class intervals of a frequency distribution have equal widths, this common width is denoted by c.
Range: this is the difference between the maximum value and the minimum value of the data set. For example, in the JC Electrics data set the maximum number of Electric Motors sold has a value of 25, while the minimum is 14. Hence, to calculate the range, you must calculate 25–14=9.