From a "below" table to classes
Some tables give running totals, not frequencies. A "below" table is one.
- Six made-up finishing times, in minutes. Each row says how many finished below that time.
- Nobody finished below 25. So 25-30 holds 4.
- Class 30-35 holds
12 − 4 = 8. - Each next class is its total minus the total before it.
The rule
Each class holds its own total minus the total before it.
The first class has no class before it. So its frequency is its own total. The problem gives the lower bound of the first class. Here nobody finished below 25.
Each "below" number is a cumulative frequency. In the row 30-35, 12 finished below 35 minutes. That counts the class and every class before it. Some books write "less than" for "below".
| Class | Below | Frequency |
|---|---|---|
| 25-30 | 4 | 4 |
| 30-35 | 12 | 12 − 4 = 8 |
| 35-40 | 24 | 24 − 12 = 12 |
| 40-45 | 44 | 44 − 24 = 20 |
| 45-50 | 54 | 54 − 44 = 10 |
| 50-55 | 60 | 60 − 54 = 6 |
Example. Find the median time. Here n = 60. Half of n is 30. The first running total to reach 30 is 44. So 40-45 is the median class.
Here l = 40 is the lower bound of 40-45. cf = 24 is the total before it. f = 20 is its frequency. h = 5 is its width. Median = 40 + ((30 − 24) ÷ 20) × 5.
Step by step: 30 − 24 = 6. Then 6 ÷ 20 = 0.3. Then 0.3 × 5 = 1.5.
That is 40 + 1.5 = 41.5 minutes.
Now try it. Find how many are in each class.
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