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Note

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.

Frequency table of soccer player height
HEIGHTS
(INCHES)
FREQUENCY RELATIVE
FREQUENCY
CUMULATIVE
RELATIVE
FREQUENCY
59.95–61.95 5 5 100 = 0.05 0.05
61.95–63.95 3 3 100 = 0.03 0.05 + 0.03 = 0.08
63.95–65.95 15 15 100 = 0.15 0.08 + 0.15 = 0.23
65.95–67.95 40 40 100 = 0.40 0.23 + 0.40 = 0.63
67.95–69.95 17 17 100 = 0.17 0.63 + 0.17 = 0.80
69.95–71.95 12 12 100 = 0.12 0.80 + 0.12 = 0.92
71.95–73.95 7 7 100 = 0.07 0.92 + 0.07 = 0.99
73.95–75.95 1 1 100 = 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:

  • 59.95 to 61.95 inches
  • 61.95 to 63.95 inches
  • 63.95 to 65.95 inches
  • 65.95 to 67.95 inches
  • 67.95 to 69.95 inches
  • 69.95 to 71.95 inches
  • 71.95 to 73.95 inches
  • 73.95 to 75.95 inches

Note

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 23 100 or 23%. This percentage is the cumulative relative frequency entry in the third row.

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[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 6 50 = 0.12 0.12
4.97–6.99 7 7 50 = 0.14 0.12 + 0.14 = 0.26
6.99–9.01 15 15 50 = 0.30 0.26 + 0.30 = 0.56
9.01–11.03 8 8 50 = 0.16 0.56 + 0.16 = 0.72
11.03–13.05 9 9 50 = 0.18 0.72 + 0.18 = 0.90
13.05–15.07 5 5 50 = 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.

Try it solutions

0.56 or 56%

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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%.

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From [link] , find the percentage of rainfall that is between 6.99 and 13.05 inches.

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0.30 + 0.16 + 0.18 = 0.64 or 64%

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Use the heights of the 100 male semiprofessional soccer players in [link] . Fill in the blanks and check your answers.

  1. The percentage of heights that are from 67.95 to 71.95 inches is: ____.
  2. The percentage of heights that are from 67.95 to 73.95 inches is: ____.
  3. The percentage of heights that are more than 65.95 inches is: ____.
  4. The number of players in the sample who are between 61.95 and 71.95 inches tall is: ____.
  5. What kind of data are the heights?
  6. Describe how you could gather this data (the heights) so that the data are characteristic of all male semiprofessional soccer players.

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.

  1. 29%
  2. 36%
  3. 77%
  4. 87
  5. quantitative continuous
  6. get rosters from each team and choose a simple random sample from each
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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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