Estimate population size using proportions

Key notes : –

1. Understanding Population and Sample

  • Population: The entire group that is being studied.
  • Sample: A smaller group selected from the population that represents the population.

2. Why Estimate Population Size?

  • Estimating the population size is important when it’s impractical or impossible to count every individual in a large population, like animals in the wild, or people in a large city.

3. Proportions in Estimation

  • The principle behind estimating population size using proportions is based on the idea that if you know the proportion of a sample, you can use that proportion to estimate the entire population’s size.
  • Proportion Formula:
  • Proportion Setup:

Learn with an example

🔴To determine the bobcat population, scientists tagged 81 bobcats. Later, they counted 700 bobcats, of which 27 had tags. To the nearest whole number, what is the best estimate for the bobcat population?

  • 🔷The ratio of marked bobcats to total bobcats should be about the same in both the sample population and the overall population. You know how many bobcats were in the sample and how many of those were marked. You also know the total number of marked bobcats.
  • Set up a proportion.
    • marked bobcats counted / total bobcats counted = total marked bobcats / estimated bobcat population
  • Plug in the numbers you know and solve for the bobcat population, p.
  • 27/100 = 81/p
  • 27/100 ( 700p ) = 81/p ( 700p ) —–> Multiply both sides by 700p
  • 27p = 81 · 700 ——> Simplify
  • 27p = 56,700 ——–> Simplify
  • p = 2,100 ———> Divide both sides by 27
  • The best estimate for the bobcat population is 2,100.

🔴 Scientists captured, tagged, and released 36 crows as part of a research study. A week later, they counted 180 crows, of which 27 had tags. To the nearest whole number, what is the best estimate for the crow population?

  • 🔷The ratio of marked crows to total crows should be about the same in both the sample population and the overall population. You know how many crows were in the sample and how many of those were marked. You also know the total number of marked crows.
  • Set up a proportion.
    • marked crows counted / total crows counted = total marked crows / estimated crow population
  • Plug in the numbers you know and solve for the crow population, p.
  • 27/180 = 36/p
  • 27/180 ( 180p ) = 36/p ( 180p ) ———> Multiply both sides by 180p
  • 27p = 36 · 180 ———> Simplify
  • 27p = 6,480 ———> Simplify
  • p = 240 ——–> Divide both sides by 27
  • The best estimate for the crow population is 240.

🔴 Wombats are animals that are native to Australia and are related to kangaroos. To estimate the wombat population, Professor Roth’s research group trapped 89 wombats and tagged them. They returned the tagged wombat to the wild, and a week later, trapped 240 wombats. Of those wombats, 24 were marked. To the nearest whole number, what is the best estimate for the wombat population?

  • 🔷 The ratio of marked wombats to total wombats should be about the same in both the sample population and the overall population. You know how many wombats were in the sample and how many of those were marked. You also know the total number of marked wombats.
  • Set up a proportion.
    • marked wombats counted / total wombats counted = total marked wombats / estimated wombat population
  • Plug in the numbers you know and solve for the wombat population, p.
  • 24/240 = 89/p
  • 24/240 ( 240p ) = 89/p ( 240p ) ——-> Multiply both sides by 240p
  • 24p = 89 · 240 ——–> Simplify
  • 24p = 21,360 ——–> Simplify
  • p = 890 ——–> Divide both sides by 24
  • The best estimate for the wombat population is 890.

Let’s practice! 🖊️