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Because of rounding, the relative frequency column may not always sum to one, and the last entry in the cumulative relative frequency column may not be one. However, they each should be close to one.
[link] represents the heights, in inches, of a sample of 100 male semiprofessional soccer players.
| HEIGHTS
(INCHES) |
FREQUENCY | RELATIVE
FREQUENCY |
CUMULATIVE
RELATIVE FREQUENCY |
|---|---|---|---|
| 59.95–61.95 | 5 | = 0.05 | 0.05 |
| 61.95–63.95 | 3 | = 0.03 | 0.05 + 0.03 = 0.08 |
| 63.95–65.95 | 15 | = 0.15 | 0.08 + 0.15 = 0.23 |
| 65.95–67.95 | 40 | = 0.40 | 0.23 + 0.40 = 0.63 |
| 67.95–69.95 | 17 | = 0.17 | 0.63 + 0.17 = 0.80 |
| 69.95–71.95 | 12 | = 0.12 | 0.80 + 0.12 = 0.92 |
| 71.95–73.95 | 7 | = 0.07 | 0.92 + 0.07 = 0.99 |
| 73.95–75.95 | 1 | = 0.01 | 0.99 + 0.01 = 1.00 |
| Total = 100 | Total = 1.00 |
The data in this table have been grouped into the following intervals:
This example is used again in Descriptive Statistics , where the method used to compute the intervals will be explained.
In this sample, there are five players whose heights fall within the interval 59.95–61.95 inches, three players whose heights fall within the interval 61.95–63.95 inches, 15 players whose heights fall within the interval 63.95–65.95 inches, 40 players whose heights fall within the interval 65.95–67.95 inches, 17 players whose heights fall within the interval 67.95–69.95 inches, 12 players whose heights fall within the interval 69.95–71.95, seven players whose heights fall within the interval 71.95–73.95, and one player whose heights fall within the interval 73.95–75.95. All heights fall between the endpoints of an interval and not at the endpoints.
From [link] , find the percentage of heights that are less than 65.95 inches.
If you look at the first, second, and third rows, the heights are all less than 65.95 inches. There are 5 + 3 + 15 = 23 players whose heights are less than 65.95 inches. The percentage of heights less than 65.95 inches is then or 23%. This percentage is the cumulative relative frequency entry in the third row.
[link] shows the amount, in inches, of annual rainfall in a sample of towns.
| Rainfall (Inches) | Frequency | Relative Frequency | Cumulative Relative Frequency |
|---|---|---|---|
| 2.95–4.97 | 6 | = 0.12 | 0.12 |
| 4.97–6.99 | 7 | = 0.14 | 0.12 + 0.14 = 0.26 |
| 6.99–9.01 | 15 | = 0.30 | 0.26 + 0.30 = 0.56 |
| 9.01–11.03 | 8 | = 0.16 | 0.56 + 0.16 = 0.72 |
| 11.03–13.05 | 9 | = 0.18 | 0.72 + 0.18 = 0.90 |
| 13.05–15.07 | 5 | = 0.10 | 0.90 + 0.10 = 1.00 |
| Total = 50 | Total = 1.00 |
From [link] , find the percentage of rainfall that is less than 9.01 inches.
0.56 or 56%
From [link] , find the percentage of heights that fall between 61.95 and 65.95 inches.
Add the relative frequencies in the second and third rows: 0.03 + 0.15 = 0.18 or 18%.
From [link] , find the percentage of rainfall that is between 6.99 and 13.05 inches.
0.30 + 0.16 + 0.18 = 0.64 or 64%
Use the heights of the 100 male semiprofessional soccer players in [link] . Fill in the blanks and check your answers.
Remember, you count frequencies . To find the relative frequency, divide the frequency by the total number of data values. To find the cumulative relative frequency, add all of the previous relative frequencies to the relative frequency for the current row.
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