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1.9 Sampling and data: frequency, relative frequency, and cumulative  (Page 2/5)

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In this sample, there are 5 players whose heights are between 59.95 - 61.95 inches, 3 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, 7 players whose height falls within the interval 71.95 - 73.95, and 1 player whose height falls within the interval 73.95 - 75.95. All heights fall between the endpoints of an interval and not at the endpoints.

From the table, 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 males 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.

From the table, 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%.

Use the table of heights of the 100 male semiprofessional soccer players. 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

Optional collaborative classroom exercise

In your class, have someone conduct a survey of the number of siblings (brothers and sisters) each student has. Create a frequency table. Add to it a relative frequency column and a cumulative relative frequency column. Answer the following questions:

  1. What percentage of the students in your class has 0 siblings?
  2. What percentage of the students has from 1 to 3 siblings?
  3. What percentage of the students has fewer than 3 siblings?

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

The following table was produced:

Frequency of commuting distances
DATA FREQUENCY RELATIVE
FREQUENCY		 CUMULATIVE
RELATIVE
FREQUENCY
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 3 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 5 or 7 miles?
  4. What fraction of the people surveyed commute 12 miles or more? Less than 12 miles? Between 5 and 13 miles (does not include 5 and 13 miles)?
  1. No. Frequency column sums to 18, not 19. Not all cumulative relative frequencies are correct.
  2. False. Frequency for 3 miles should be 1; for 2 miles (left out), 2. 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.
  3. 5 19
  4. 7 19 , 12 19 , 7 19
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Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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