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The data can be put in order from lowest to highest: 20, 68, 80, 92.

The differences between the data have meaning. The score 92 is more than the score 68 by 24 points. Ratios can be calculated. The smallest score is 0. So 80 is four times 20. The score of 80 is four times better than the score of 20.

Frequency

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

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

[link] lists 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 value of the data occurs. According to [link] , there are three students who work two hours, five students who work three hours, and so on. The sum of the values in the frequency column, 20, represents the total number of students included in the sample.

A relative frequency is the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes. 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 with relative frequencies
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 values in the relative frequency column of [link] 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 tothe relative frequency for the current row, as shown in [link] .

Frequency table of student work hours with relative and cumulative relative frequencies
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.

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

Questions & Answers

wat improvement do economic has with our life
Aminata Reply
it help us how to use our limited resources to satisfy our unlimited wants
Pagnol
Economics is the social Science in which we study how scarce resources are allocated for the betterment of human being.
Ali Reply
what is equilibrium point
Happiness Reply
where price and quantity demanded meet
Pagnol
is the point where price an quantity demanded meet
Aminata
why do consumer demand curve tend to move downward slope
Aminata
What is monopoly
Ezekiel Reply
what is economics
BUKENYA Reply
economics us behavior. Of people, nations, markets etc. It has much to do with reactions. watch MSNBC. Bloomberg. everyday they talk about how the markets react to an piece of news, legislation, interest rates etc. Interesting volatile stuff
TOM
but, it also react with science
ezhilarasan
economic is a science with study's the behavior of people,market and price
Bertilla
it's a science which study the behavior of people ,market n price
Bertilla
What is opportunity cost?
Junior
opp. cost~a benefit, profit or value of something that must be given up to acquire or achieve something else
Kim
or something that you foregone
Kim
who is the father of economic
Yirtutey Reply
Adam smith
shaikh
modern father is Adam smith
Bilal
Adam smith
Nazifi
what is backward bend
Florence Reply
It's a curve that reverses direction
Ajibade
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Kojo
Evening
Ajibade
evening
Emmanuel
hi
Lawrence
Any Nigerian lady to meet here Well on eco ground
Suleiman
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Kojo
hello
James
yeah
Kojo
how?
Kojo
how time
James
cool
Kojo
Ok
James
Good morning
Junior
morning all
Emeka
Morning
Ajibade
😶g
Maaz
moaz taha u r egyptian aren't u ?
Marwa
marwa no
Maaz
how economic effect the Market
Abdikarem
what is the difference between statistic and statistics?
Shafiu
it can can be described as when the demand is insufficient
Amaan Reply
high Dublin divino through Higginbotham
Shubham Reply
How does exchange rate affect the demand and supply?
austine
You mean demand and supply of currency ?
Jahangir
Hello
Hann
Hi
Jahangir
Am debby
Hann
am jahangir
Jahangir
how are you
Ogunsola
I am All fine Wbu ?
Jahangir
doing great
Ogunsola
Hw r u all
Mudassar
Am gud
Hann
Gd
Mudassar
Ogunsola
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Mutha
hi
Hammed
Hello
Assan
hi
Pranshi
Hello
Kamal
hi
Pranshi
hi
Abbas
hi
Abdirazak
ki sah botine
Neyshawn
hi
Nasir
Hello Economist
Nasir
hello
Victor
Hie... may anyone give me examples of countries that successfully implemented import substitution industrialisation.
Thabo
Nigeria
Junior
hey I'm emma from Uganda
niwagaba
Hello
Abraham
What is the difference between Demand and Quantity Demanded?
Weedh
Demand refers to how much a product is desired by buyer mean while quantity demanded refers to the amount of product a buyer is willing to buy at a certain price.
Junior
Good evening
Ajibade
Evening
Junior
evening
Ogunsola
someone wat is d textbook to read for banking and finance course
ayomide
Evening
Anjorin
Hw r u doing
Faku
yh
Benj
I'm good, u?
Anjorin
demand is the various quantity of goods or services a consumer is Willing and able to buy at a particular price over s given period of time while quantity demanded is the amount of goods or services being paid for
Florence
Good
Awudu
1.it allows producers to learn and invent 2.it allows agent to take advantage of economic scale 3.it allow agents to focus in areas of
oyebola Reply
can someone explain the motive of money to me?
Alemogho Reply
ask the question you don't know
ojo
opportunity cost
Sylvo
the motive of money is to pay for goods or services. it's also for transaction purposes bet it ordinary or unforseen
Silke
Money helps to reduce our scarcity problems. It can satisfy your wants to an extent
Okwori
transactive motive
Aminata
money help as a store of value for future uses
Pagnol
it also serve as a medium of exchange
Pagnol
How dose economics use science methods to explains it problems
Edmond Reply
according to Jhon Robinson the main problem of economics is what to produce? how to produce? whom to produce? economics tries to solve these problem scientifically by using its theories which are scientific in nature,basically micro and macro theories which just explain what the problem is...
Lavkesh
and now the solving techinique is also changed. only theories or its matematical +statistical version is not sufficient so the economist had developed Econometrics which includes economic theory+mathematical economics+statistics, for solving economic problem. This method treats economics as a pure
Lavkesh
..pure science so this technique is based on pure scientific methods.
Lavkesh
Economics is the scientific study of human behavior so there for science is used to solve economics problems using economics theories
Florence
economic is not higly subject of taminadu ...
Mutha
measurement of elasticity of demand
John Reply
Price elasticity of demand= Percentage change in quantity demanded/ Percentage change in price
Jale
For example, suppose that a 10 percent increase in the price of an ice-cream cone causes the amount of ice cream you buy to fall by 20 percent. We calculate your elasticity of demand as
Jale
Price elasticity of demand =20 percent /10 percent = 2
Jale
In this example, the elasticity is 2, reflecting that the change in the quantity demanded is proportionately twice as large as the change in the price.
Jale
what is economic
Samuel Reply
economics is a social science that studies the relationship of human behavior between ends and scare...
Lawrence
Why is economics as a subject is so important to human being?
austine
it's significant in study of managing available resources to satisfy human needs and wants
mohamed
economics is the science of wealth
Aamir
it is also said that it is the science of scarcity
Aamir
why study economic
Neo
Economic helps to meet our needs and wants nd to make choices.
Abraham
careers or jobs associated with economics
Neo
Economics is more than choices, scarcity, resources etc. It has a lot to do with psychology, social psychology. Understand motivation for consumer decisons.
TOM
okey
Neo
I what to study economic understand education what subject will I take in my jamb
DIRIOHA
English.mathematics.economics and one other social science subject
Ogunsola
economic is life start to end
Mutha
Plz help in lectures job for economics
Mudassar
acc to robbin . "Economics is a science that studies human behaviour as a relationship between scarce means and ends which have alternative uses"
Jahangir
Economics is important to man "human wants are insatiable
Hann
pleas explain circular flow of income
Eagle
what is economic growth
Samuel
Economic growth is an increase in the real output leading to a growth or a rise in the nations gdp.
Charles
Economics is the study of wealth or money and it's an economic activity which has almost three terms divided into them, production consumption and Distribution of wealth.
Zahid
Economics is the study of wealth or money and it's an economic activity which has almost three terms divided into them, production consumption and Distribution of goods and services.
Zahid
plz what is econometrix
saheed
How does commercial banks create credit
Penda Reply
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Source:  OpenStax, Introductory statistics. OpenStax CNX. Aug 09, 2016 Download for free at http://legacy.cnx.org/content/col11776/1.26
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