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1.8 Frequency

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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.

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 or proportion 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/ relative 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 relative 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 0.30 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 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
This example is used again in the Descriptive Statistics chapter, where the method used to compute the intervals will be explained.

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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