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Rates. STA 220 – Lecture #3. Rates. How do we compare the birth rate of a large country, such as China, with a small country, such as Iceland? How do we compare how much the state of California spends on education versus the amount spent by Wyoming?. Computation of Rates.

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Rates

Rates

STA 220 – Lecture #3


Rates1

Rates

  • How do we compare the birth rate of a large country, such as China, with a small country, such as Iceland?

  • How do we compare how much the state of California spends on education versus the amount spent by Wyoming?


Computation of rates

Computation of Rates

  • Rates are used instead of

  • Suppose “x” rate we’re interested in was the birth rate of RI in 1999. Suppose that 12,000 babies were born in 1999 and that the population of RI was 1,000,000.


Computation of rates1

Computation of Rates


Computation of rates2

Computation of Rates

  • Had we used the constant 10,000 then we would have 120 births per 10,000

  • For consistency, the multiple of 1,000 has been adopted as the de facto standard for population rates

  • When comparing rates,


Computation of rates3

Computation of Rates


Computation of rates4

Computation of Rates

  • Population: 1,000,000

  • Births: 12,000

  • Deaths: 11,000

  • Immigrants: 600

  • Emigrants: 1,700


Computation of rates5

Computation of Rates


Computation of rates6

Computation of Rates


Computation of rates7

Computation of Rates


Computation of rates8

Computation of Rates


Computation of rates9

Computation of Rates


Combining rates

Combining Rates

  • Suppose you had the following birth rate information for CT and were asked to compute a regional birth rate for both RI and CT, combined.

    • CT population: 8,000,000

    • CT births: 160,000

      What is CT’s birth rate?


Combining rates1

Combining Rates


Combining rates2

Combining Rates


Rare events

Rare Events

  • In the above rates, multiplying by 1000 generally made the rates meaningful

  • Suppose the breast cancer death rate is 0.012 per 1,000 women…

  • Instead

    • Breast cancer death rate of 12 deaths per 1,000,000 women

    • Note the rate is now per 1,000,000 because the per “xx” rate corresponds to


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