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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%

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.

Try it solutions

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.

  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

Nineteen people were asked how many miles, to the nearest mile, they commute to work each day. The data are as follows:

  • 2
  • 5
  • 7
  • 3
  • 2
  • 10
  • 18
  • 15
  • 20
  • 7
  • 10
  • 18
  • 5
  • 12
  • 13
  • 12
  • 4
  • 5
  • 10
. [link] was produced:

Frequency of commuting distances
3 3 3 19 0.1579
4 1 1 19 0.2105
5 3 3 19 0.1579
7 2 2 19 0.2632
10 3 4 19 0.4737
12 2 2 19 0.7895
13 1 1 19 0.8421
15 1 1 19 0.8948
18 1 1 19 0.9474
20 1 1 19 1.0000
  1. Is the table correct? If it is not correct, what is wrong?
  2. True or False: Three percent of the people surveyed commute three miles. If the statement is not correct, what should it be? If the table is incorrect, make the corrections.
  3. What fraction of the people surveyed commute five or seven miles?
  4. What fraction of the people surveyed commute 12 miles or more? Less than 12 miles? Between five and 13 miles (not including five and 13 miles)?
  1. No. The frequency column sums to 18, not 19. Not all cumulative relative frequencies are correct.
  2. False. The frequency for three miles should be one; for two miles (left out), two. The cumulative relative frequency column should read: 0.1052, 0.1579, 0.2105, 0.3684, 0.4737, 0.6316, 0.7368, 0.7895, 0.8421, 0.9474, 1.0000.
  3. 5 19
  4. 7 19 , 12 19 , 7 19

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Source:  OpenStax, Business statistics -- bsta 200 -- humber college -- version 2016reva -- draft 2016-04-04. OpenStax CNX. Apr 05, 2016 Download for free at http://legacy.cnx.org/content/col11969/1.5
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