Teaching and Learning Quantitative Reasoning

**Thinking Quantitatively Project 2: ***Dependency Ratios*

In this project you will explore the construction of 3 separate statistics using demographic data. This will be a written project, no Excel; you will hand in hard copy in class and you may leave space to write in any computational work performed. The following ratios have been computed using the derivation rules for the United States in **2002**:

· The age dependency ratio, 59.8, is derived by dividing the combined under-18 and 65-and-over populations by the 18-to-64 population and multiplying by 100. |

· The old-age dependency ratio, 19.3, is derived by dividing the population 65 and over by the 18-to-64 population and multiplying by 100. |

· The child dependency ratio, 40.5, is derived by dividing the population under 18 by the 18-to-64 population and multiplying by 100. |

- Determine the
**current****populations,**in the three different age categories used for these ratios, using the census.gov webpage: http://www.census.gov/population/age/data/2011comp.html by**select age groups**(use the Census table for “Age and Sex Composition”).

- Compute the three different dependency
**ratios**using the current population estimates and the derivation rules above.

- Are these ratios part-to-part or part-to-whole? Explain in one or two coherent sentences.

- The article,
*Europeans Fear Crisis May Threaten Liberal Benefits*, http://www.nytimes.com/2010/05/23/world/europe/23europe.html?pagewanted=1&th&emc=th , contains the following graphic. How does this graphic compare to the dependency ratios you computed in**#2**above?

- The derivation rules seem to be giving a
**percentage**. Explain how it is possible to interpret each of these ratios as a percentage. Be sure to use each number in a sentence, don’t just talk in generalities.

- What significance does each ratio have, i.e. why would someone bother to compare the populations of the relevant age categories? Explain in one or two coherent sentences for each ratio under consideration.

- Which of these ratios would increase as the population of the US
*continues to age*? Explain in one or two coherent sentences for each ratio under consideration. Note: the aging of our population does**not**refer to the fact that everyone is getting older! It means that the**percentage**of our population that is 65 and older is increasing.

- Find population estimates of the three age categories for the year 2050 (search for population projections) and re-compute the ratios.

- Ireland experienced a recent economic boom in the 1990’s, and some have attributed this to a declining age dependency ratio. Explain why this makes sense in a few coherent sentences.

- Use the world factbook: https://www.cia.gov/library/publications/the-world-factbook/ to compute the dependency ratios for Ireland.

- The age structure breakdown given in the world factbook is 0-14 and 15-64, which is different from the under 18 age breakdown above. How will the different age structure affect each ratio? Write a sentence for each ratio under consideration.

- How do you think the dependency ratios for a Third World country would compare to the United States? Explain why you think so in a sentence or two for each ratio under consideration.

- Once again use the world factbook to compute the dependency ratios for a Third World country. Analyze your predictions from #11 in a sentence or two. How accurate were you?

- Imagine you have to write a brief
**1 page**article for the online school newspaper on dependency ratios. Write such an article using any of the information above that you find relevant (this is a QR class, you should include some statistics!). Be sure to include a catchy title for your article J

Please include the following:

- Identify a statistic we should know and its precise definition.
- Present a few cogent reasons why you believe the statistic is important.
- Make the number meaningful for your reader (e.g. by restating in more easily grasped terms or by making comparisons).
- Provide source information for you number, the reference librarians can be of assistance in helping you locate and search statistical databases.
- Answer Joel Best’s 3 questions we should ask of any statistic:
- Who created the statistic?
- Why did they create it?
- How did they create it?

- Discuss the “dark figure” associated to this statistic and any false positives/negatives resulting from the definition.

The paper should be coherent and structured. It should have a meaningful title, an introduction, and a conclusion. Be certain to support your claims with evidence, to exercise appropriate caution in your arguments, and to acknowledge uncertainty and complexity were relevant. Anticipate and address the reasonable questions of the critical reader.

You will be graded using the following rubric:

- Number selection: appropriateness and significance of the topic [10]
- Reasons supporting number importance: quality and clarity [10]
- Number presentation: definition and comparative contrasts [10]
- Source information: identification and reliability evaluation, who/why/how [10]
- Paper organization: structure, opening and closing [20]
- Writing quality: grammar, word usage, sentence focus [20]
- Argument quality: statement clarity and evidence for claims [10]
- Complexity: uncertainties recognized and questions raised, dark figure, false negatives/positives [10]

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What did you have your students compute in #10 from the World Factbook? Did they pick a country of their choice?

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Oops sorry about that! I left out the last word, it is for “Ireland”, I have them pick a “3rd world country” of their choice in #13, but in #10 wanted everyone to look at the same country (Ireland). Thanks for catching that.

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I dont understand how to work these out, can someone help me

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Hi Crystin I am assuming you are a student working on this for a class? To compute the ratios, remember that you are simply comparing the number of people in one group to the number of people in another group. So if there are 500 people over 64 and 1,500 people 18-64, the ratio is 500 : 1,500 or 33.3 : 100.

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I’m so confused on #4. I’m a student working on the project. The graphics are basically showing the pension crisis. Can someone help me?

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Pay attention to how things are defined. If we take the ratio of births to people we may get 12.5 births per 1,000 people. But if we flip the ratio, people to births, then we get 1,000 people : 12.5 births or 80 people per birth.

The order matters even though the two quantities you are comparing are EXACTLY the same.

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ok so say I get for the child dependency percentage is 41.1% and say its out of 100-since order matters. it would be 100:41.1? which would be 2.4?

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Correct, and remember these are part to part ratios so using a percentage is tricky! The ratio might be 41.1 “dependents” per 100 working age people, which can be flipped to 2.4 workers per dependent. The graph is going down, meaning the number of workers per dependent is declining… not good news for your social security account!

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thank you so much. this really helped me.

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Can you give me some help with number 7 and number 11. how I should go about those 2 answers?

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If you represent your ratios as fractions think about how a fraction could increase. If you are looking at the birth rate comparing births to the number of women of child bearing age (15-44), then the birth rate could increase next year if the number of births go up OR the number of women of child bearing age goes down.

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what about number 11? do you have any advice for that one?

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for #5 how would I do this question

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The 59.8 d-ratio given at the top is a part to part ratio, 59.8 : 100. These are tricky. If the ratio of girls to boys is 60 : 100 you are tempted to say 60% of the class are girls but this is incorrect (or 60% of the boys are girls but this is silly). Instead we have to say the number of girls is 60% of the number of boys.

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I do you do number 1 and 2 do you just add them up

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How do you do the first 4? I am really confused. I am a student trying to work through this.

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The key is to realize we are splitting the population up into 3 groups: young, middle, old. You are just being asked to compare the sizes of the three groups (the word dependency confuses some students, it just means the old and young can be thought of as “dependents”).

Example: young = 40, middle = 120, old = 10

Old : middle 10 : 120 = 1/12 = 0.083 = 8.3 : 100

Young : middle 40 : 120 = 1/3 = 33.3 : 100

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Thanks! so the format should be 37.3:100 36.1:100 38.5:100

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It depends on the wording of the question. So if they are giving dependency ratios as “57” then that means 57 : 100, but you would want to answer with “37.3” instead of 37.3 : 100.

Best wishes!

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So for the first question, I just need a little more clarity. What numbers am I supposed to be looking for?

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Can anyone explain questions 8,9, and 10?

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