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absolute and relative quantities

Quantitative Reasoning - DePaul University. 2. Introduction. There are two ways to measure numerical data

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absolute and relative quantities

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    1. Quantitative Reasoning - DePaul University 1 AbsoluteandRelativeQuantities

    2. Quantitative Reasoning - DePaul University 2

    3. Quantitative Reasoning - DePaul University 3 ABSOLUTE QUANTITIES The absolute quantity of a quantifiable variable is a measure of the absolute occurrence of the variable.

    4. Quantitative Reasoning - DePaul University 4 The EXCEL file StateLotteries2000.xls shows ticket sales. When they are sorted in ascending order, we can see which states have the least and greatest ticket sales in absolute terms. 2000 Ticket Absolute State Population Sales Sales Montana 902,000 $ 29,900,000 $ 29,900,000 Nebraska 1,711,000 $ 68,170,000 $ 68,170,000 Vermont 609,000 $ 75,920,000 $ 75,920,000 California 33,872,000 $ 2,598,380,000 $ 2,598,380,000 Texas 20,852,000 $ 2,657,290,000 $ 2,657,290,000 New York 18,976,000 $ 3,629,260,000 $ 3,629,260,000 Massachusetts 6,349,000 $ 3,697,970,000 $ 3,697,970,000

    5. Quantitative Reasoning - DePaul University 5 Conclusion Montana spent the least on lottery tickets, while Massachusetts spent the most.

    6. Quantitative Reasoning - DePaul University 6 RELATIVE QUANTITIES The relative quantity of a quantifiable variable is a measure of the absolute occurrence of the variable in relation to some other quantifiable variable.

    7. Quantitative Reasoning - DePaul University 7 We can measure ticket sales by taking the absolute ticket sales of each state and dividing by the state population. This ratio is the relative ticket sales. 2000 Ticket Relative State Population Sales Sales Montana 902,000 $ 29,900,000 $33.15 Nebraska 1,711,000 $ 68,170,000 $39.84 Arizona 5,131,000 $ 255,550,000 $49.81 New Mexico 1,819,000 $ 110,610,000 $60.81 Massachusetts 6,349,000 $ 3,697,970,000 $582.45 Delaware 784,000 $ 556,450,000 $709.76 South Dakota 755,000 $ 581,050,000 $769.60 Rhode Island 1,048,000 $ 864,320,000 $824.73

    8. Quantitative Reasoning - DePaul University 8 Conclusion Once the relative ticket sales for each state is sorted in ascending order, we reach very different conclusions about which states have the least and greatest ticket sales (relative to the state’s population). Montana again spent the least on lottery tickets, while Rhode Island spent the most—in terms of relative sales.

    9. Quantitative Reasoning - DePaul University 9 Summary Many data sets can be analyzed according to various quantitative measures that produce different conclusions. In general, examining relative quantities is more informative than absolute quantities. The change found is an increase if new value > previous value The change found is a decrease if new value < previous value

    10. Quantitative Reasoning - DePaul University 10 RATIOS Suppose we wish to compare the size of California’s population to that of Oregon’s. According to the 2000 census, California was home to 33,872,000 people, while 3,421,000 resided in Oregon. Clearly many more people call California home than Oregon. Open your presentation with an attention-getting incident. Choose an incident your audience relates to. The incidence is the evidence that supports the action and proves the benefit. Beginning with a motivational incident prepares your audience for the action step that follows.Open your presentation with an attention-getting incident. Choose an incident your audience relates to. The incidence is the evidence that supports the action and proves the benefit. Beginning with a motivational incident prepares your audience for the action step that follows.

    11. Quantitative Reasoning - DePaul University 11 RATIOS If we compute the ratio of California’s population to Oregon’s we have Ratio = 33,872,000/3,421,000 = 9.90 What does this mean? It means that California’s population is almost ten times as big as Oregon’s. Open your presentation with an attention-getting incident. Choose an incident your audience relates to. The incidence is the evidence that supports the action and proves the benefit. Beginning with a motivational incident prepares your audience for the action step that follows.Open your presentation with an attention-getting incident. Choose an incident your audience relates to. The incidence is the evidence that supports the action and proves the benefit. Beginning with a motivational incident prepares your audience for the action step that follows.

    12. Quantitative Reasoning - DePaul University 12 Changes in a Quantity over Time Open your presentation with an attention-getting incident. Choose an incident your audience relates to. The incidence is the evidence that supports the action and proves the benefit. Beginning with a motivational incident prepares your audience for the action step that follows.Open your presentation with an attention-getting incident. Choose an incident your audience relates to. The incidence is the evidence that supports the action and proves the benefit. Beginning with a motivational incident prepares your audience for the action step that follows.

    13. Quantitative Reasoning - DePaul University 13 Data Types Each column represents a different kind of data: Column A Country Categorical Column B Area Quantitative Column C 1980 Population Quantitative Column D 1990 Population Quantitative Column E 2000 Population Quantitative What units are the data expressed in?

    14. Quantitative Reasoning - DePaul University 14 Changes in populations between different time periods We can describe this change by using an absolute change or a relative change to describe either a net gain or a loss.

    15. Quantitative Reasoning - DePaul University 15 Absolute Change Absolute change is defined as the difference from a previous value to a new value. For example, the change of population for Afghanistan between 1980 and 1990. Absolute change = 1990 pop – 1980 pop Absolute change = 14,750,000 – 14,985,000 Absolute change = –235,000 What does the –235,000 represent in terms of the problem?

    16. Quantitative Reasoning - DePaul University 16 Relative Change The relative change is defined as the absolute change divided by the previous value. For example, the relative change for the Afghanistan’s population is given by Relative change = Absolute change/previous Relative change = (new – previous)/previous Relative change = (14750 – 14985)/14985 Relative change = –235/14985 Relative change = –0.0156823

    17. Quantitative Reasoning - DePaul University 17 Percent Change We can express relative change as percent change by multiplying by 100%, or Percent change = Relative change * 100% For our previous example, we have that Percent change = –0.0156823 * 100% Percent change ˜ –1.57% What does this percent change mean?

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