# 1.3 Levels of measurement  (Page 2/14)

 Page 2 / 14

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 $\frac{3}{20}$ or 0.15
3 5 $\frac{5}{20}$ or 0.25
4 3 $\frac{3}{20}$ or 0.15
5 6 $\frac{6}{20}$ or 0.30
6 2 $\frac{2}{20}$ or 0.10
7 1 $\frac{1}{20}$ or 0.05

The sum of the values in the relative frequency column of [link] is $\frac{20}{20}$ , 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 $\frac{3}{20}$ or 0.15 0.15
3 5 $\frac{5}{20}$ or 0.25 0.15 + 0.25 = 0.40
4 3 $\frac{3}{20}$ or 0.15 0.40 + 0.15 = 0.55
5 6 $\frac{6}{20}$ or 0.30 0.55 + 0.30 = 0.85
6 2 $\frac{2}{20}$ or 0.10 0.85 + 0.10 = 0.95
7 1 $\frac{1}{20}$ 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 $\frac{5}{100}$ = 0.05 0.05
61.95–63.95 3 $\frac{3}{100}$ = 0.03 0.05 + 0.03 = 0.08
63.95–65.95 15 $\frac{15}{100}$ = 0.15 0.08 + 0.15 = 0.23
65.95–67.95 40 $\frac{40}{100}$ = 0.40 0.23 + 0.40 = 0.63
67.95–69.95 17 $\frac{17}{100}$ = 0.17 0.63 + 0.17 = 0.80
69.95–71.95 12 $\frac{12}{100}$ = 0.12 0.80 + 0.12 = 0.92
71.95–73.95 7 $\frac{7}{100}$ = 0.07 0.92 + 0.07 = 0.99
73.95–75.95 1 $\frac{1}{100}$ = 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

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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.
what is equilibrium point
where price and quantity demanded meet
Pagnol
is the point where price an quantity demanded meet
Aminata
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Aminata
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what is economics
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
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ezhilarasan
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Bertilla
it's a science which study the behavior of people ,market n price
Bertilla
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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
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shaikh
Bilal
Nazifi
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It's a curve that reverses direction
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Kojo
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Emmanuel
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Lawrence
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Abdikarem
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it can can be described as when the demand is insufficient
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How does exchange rate affect the demand and supply?
austine
You mean demand and supply of currency ?
Jahangir
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Hann
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Hann
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Ogunsola
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Victor
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Thabo
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Junior
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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
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Evening
Junior
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Ogunsola
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ayomide
Evening
Anjorin
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Faku
yh
Benj
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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
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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
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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
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Lavkesh
Economics is the scientific study of human behavior so there for science is used to solve economics problems using economics theories
Florence
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Mutha
measurement of elasticity of demand
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
economics is a social science that studies the relationship of human behavior between ends and scare...
Lawrence
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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
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Neo
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Abraham
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Neo
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DIRIOHA
English.mathematics.economics and one other social science subject
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Jahangir
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Hann
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Eagle
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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
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saheed
How does commercial banks create credit
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