Chapter 3A Numbers in the Real World

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Chapter 3ANumbers in the Real World

• Uses and Abuses of Percentages
• Jackie Schrag

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Uses and Abuses of Percentages

• The most common way of communication quantitative
  information is with percentages.
• A percentages is simply a fraction.
• In this lesson we will investigate some of the
  uses and abuses of percentages.

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Relative change

• Describes the size of the absolute change In
  comparison to the reference value.
• Relative change absolute change new value -
  reference value
• reference value
  Reference value

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Absolute change

• Describes the actual increase or decrease from a
  reference value to a new value.
• Absolute change new value - reference value

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Example 1

• In a 1 year period for WalMarts stock doubled
  in price from 50 to 100. What were the absolute
  and relative changes in the stock price?
• Absolute new value (100) - reference value
  (50) 50
• Relative absolute change 50

1 100
reference value
50
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Example 2

• The population of United States in 1995 was 2
  billion, then at 2000 the population increased up
  to 4 billion. What is the US population relative
  and absolute change form 1995 to 2000?
• Absolute change 4 billion - 2 billion 2
  billion
• Relative change 4 billion - 2 billion

1 100
2 billion
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Absolute Difference

• Describes the actual amount by which the compared
  value is later or smaller than the reference
  value it is the difference between these two
  values
• Absolute difference compared value - reference

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Relative Difference

• Describes the size of the absolute difference in
  comparison to the reference value
• relative difference absolute difference
• compared value -
  reference value

Reference value
Reference value
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Example 3

• The life expectancy for American men is 74 years,
  while the Russian mens life expectancy is 60
  years. Compare the life expectancy of American
  men to that of Russian men in absolute and
  relative terms.
• Absolute Difference compared value - reference
  value
• 74 - 60
• 14 years

Relative difference compared value - reference
value
Reference value
74 - 60
60
.23 23
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Example 4

• Average for full-time wage earners varies from
  state to state. As of 1998, Michigan ranked first
  in average pay, at 35,600 per person. While
  South Dakota has the lowest average pay, at
  20,500 per person. Compare average pat I South
  Dakota to that in Michigan in both absolute and
  relative terms.
• Solution Based on the wording of the statement,
  we use South Dakota pay as the compared value and
  Michigan pay as the reference value.

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Example 4 cont..

• Absolute difference compared value - reference
  value
• 20,500 -
  35,600
• - 15100
• Relative difference compared value - reference
  value

Reference value
20,500 - 35,600

35,600
-.424 -42.45
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Of versus More Than

• If the compared value is P more than the
  reference value, it is (100 P) of the
  reference value.
• If the compared value is P less than the
  reference value, it is (100 - P) of the
  reference value.

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Example 5

• Anne earns 50 more than Steven. How many times
  larger is her income than his?
• We used the rule that P more than means (100
  P) of since Anne's income is 60 more than
  Steven's, we set P 60. Thus, Carols income is
  160 of Steven's income. Remembering that 160
  1.6, we know that Anne earns 1.6 times as much at
  Steven.

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Example 6

• JC Penny's is having a 50 off sale on
  everything in the store. How does this price
  compare to its original price?
• SolutionThe 50 off means that an item sale
  price is 50 less than its original price. Thus,
  the sale price is (100 - 50) 50 off the
  original price. For example if the original price
  is 100, the sale price is 50.

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Percentage Points vs..

• When you see a change or difference expressed in
  percentage points you can assume it is an
  absolute change or difference. If it is expressed
  with the sign or the word percent, it should be
  a relative change or difference.

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Example 7

• According to time magazine story, the of adults
  reading daily news papers fell form 79 in 1970
  to 65 in 1995. Describe the change in newspaper
  readership.
• Solution the drop in readership form 79 to 65
  represents the decline of 14 percentage points.
  This is the absolute change in the percentage of
  adults who read a daily news paper. The relative
  change in readership is

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Cont.. example 7

• New value - reference value 65 - 79

-.18 -18

78
reference value
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Solving percentage problems

• If the compared value is P more than the
  reference value, then
• reference value
• and...
• compared value

Compared value

(100 P)
(100 P) X reference value
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Example 8

• You purchase a shirt with a labeled (pre-tax)
  price of 16. The local sales tax rate is 4.
  What is your final cost (including tax)?
• Your receipt shows that you paid 19.25 for a DVD
  movie, tax included. The local sales tax rate is
  6. What was the labeled (pre-tax) price of the
  DVD?

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Cont.. example 8

• When we substitute the given labeled price of
  16, the final cost is
• Final cost (104 X 16 1.04 X 16 16.64
• we are given the final cost of 19.25. We find
  the labeled price by dividing both sides by 106
• Labeled Price

Final cost 19.25 19.25


18.16
106 106 1.06
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THANK YOU(thank you)