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This module introduces the concepts of frequency, relative frequency, and cumulative relative frequency, and the relationship between these measures. Students will have the opportunity to interpret data through the sample problems provided.Labs modified to include minitabs.

Twenty students were asked how many hours they worked per day. Their responses, in hours, are listed below:

  • 5
  • 6
  • 3
  • 3
  • 2
  • 4
  • 7
  • 5
  • 2
  • 3
  • 5
  • 6
  • 5
  • 4
  • 4
  • 3
  • 5
  • 2
  • 5
  • 3

Below is a frequency table listing the different data values in ascending order and their frequencies.

Frequency table of student work hours
DATA VALUE FREQUENCY
2 3
3 5
4 3
5 6
6 2
7 1

A frequency is the number of times a given datum occurs in a data set. According to the table above, there are three students who work 2 hours, five students who work 3 hours, etc. The total of the frequency column, 20, represents the total number of students included in the sample.

A relative frequency is the fraction of times an answer occurs. To find the relative frequencies, divide each frequency by the total number of students in the sample - in this case, 20. Relative frequencies can be written as fractions, percents, or decimals.

Frequency table of student work hours w/ realative frequency
DATA VALUE FREQUENCY RELATIVE FREQUENCY
2 3 3 20 or 0.15
3 5 5 20 or 0.25
4 3 3 20 or 0.15
5 6 6 20 or 0.30
6 2 2 20 or 0.10
7 1 1 20 or 0.05

The sum of the relative frequency column is 20 20 , or 1.

Cumulative relative frequency is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row.

Frequency table of student work hours w/ relative and cumulative frequency
DATA VALUE FREQUENCY RELATIVE FREQUENCY CUMULATIVE RELATIVE FREQUENCY
2 3 3 20 or 0.15 0.15
3 5 5 20 or 0.25 0.15 + 0.25 = 0.40
4 3 3 20 or 0.15 0.40 + 0.15 = 0.55
5 6 6 20 or 0.10 0.55 + 0.30 = 0.85
6 2 2 20 or 0.10 0.85 + 0.10 = 0.95
7 1 1 20 or 0.05 0.95 + 0.05 = 1.00

The last entry of the cumulative relative frequency column is one, indicating that one hundred percent of the data has been accumulated.

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.

The following table represents the heights, in inches, of a sample of 100 male semiprofessional soccer players.

Frequency table of soccer player height
HEIGHTS (INCHES) FREQUENCY OF STUDENTS RELATIVE FREQUENCY CUMULATIVE RELATIVE FREQUENCY
Total = 100 Total = 1.00
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

The data in this table has been grouped into the following intervals:

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

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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Source:  OpenStax, Collaborative statistics (with edits: teegarden). OpenStax CNX. Jul 20, 2009 Download for free at http://legacy.cnx.org/content/col10561/1.3
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