Estimate population size using proportions
key points :
🔢 What is Estimating Population Size?
- It means finding an approximate number of people, animals, or objects in a large group.
- We use samples and proportions instead of counting everyone.
📦 What is a Sample?
- A sample is a small part of the whole population.
- It should be fair and random 🎯 so it represents the whole group.
📊 What is a Proportion?
- A proportion compares a part to the whole.
- Written as a fraction, ratio, or percentage (e.g., 3/10, 3:10, 30%).
🔁 Why Use Proportions?
- Counting large populations is hard and time-consuming ⏳
- Proportions help us estimate quickly and easily ⚡
🧮 Steps to Estimate Population Size
1️⃣ Choose a random sample from the population
2️⃣ Count the number with a specific feature
3️⃣ Write the proportion
4️⃣ Use the same proportion to estimate the total population
📘 Simple Example
- In a sample of 20 students, 5 wear glasses 👓
- Proportion = 5/20 = 1/4
- If the whole school has 400 students
- Estimated students with glasses = 1/4 × 400 = 100 🎉
🌱 Real-Life Uses
- Counting fish in a pond 🐟
- Estimating tree population in a forest 🌳
- Finding number of people in a city 🏙️
- Studying wildlife and environment 🦋
⚠️ Remember!
- The better the sample, the better the estimate ✅
- Estimates are close values, not exact numbers 🎯
🎨 Quick Tip for Students:
👉 Think small → big using proportions!
👉 Sample smartly and estimate confidently 😄📐
Learn with an example
✏️ For a research project on the local skunk population, 120 skunks were tagged and set free. Later, volunteers returned to the site and found 18 tagged skunks out the 450 skunks they counted. To the nearest whole number, what is the best estimate for the skunk population?
The ratio of marked skunks to total skunks should be about the same in both the sample population and the overall population. You know how many skunks were in the sample and how many of those were marked. You also know the total number of marked skunks.
marked skunks counted / total skunks counted = total marked skunks / estimated skunk population
Plug in the numbers you know and solve for the skunk population, p.
18/450 = 120/p
18/450 ( 450p ) = 120/p ( 450p ) Multiply both sides by 450p
18p = 120 · 450 Simplify
18p = 54,000 Simplify
p = 3,000 Divide both sides by 18
The best estimate for the skunk population is 3,000.
✏️ For a research study on various types of lizards, scientists wanted to estimate the local skink population. They captured, marked, and released 26 skinks. A week later, the scientists returned to the site and found 10 marked skinks out of the 150 skinks they counted. To the nearest whole number, what is the best estimate for the skink population?
The ratio of marked skinks to total skinks should be about the same in both the sample population and the overall population. You know how many skinks were in the sample and how many of those were marked. You also know the total number of marked skinks.
Set up a proportion.
marked skinks counted / total skinks counted = total marked skinks / estimated skink population
Plug in the numbers you know and solve for the skink population, p.
10/150 = 26/p
10/150 ( 150p ) = 26/p ( 150p ) Multiply both sides by 150p
10p = 26 · 150 Simplify
10p = 3,900 Simplify
p = 390 Divide both sides by 10
The best estimate for the skink population is 390.
✏️ For a science fair project, a group of students decides to estimate the population of hedgehogs living in the nearby forest. They trap 69 hedgehogs and mark them. Then, a week later, they return to the forest and trap 1,000 hedgehogs, 23 of which are marked. To the nearest whole number, what is the best estimate for the hedgehog population?
The ratio of marked hedgehogs to total hedgehogs should be about the same in both the sample population and the overall population. You know how many hedgehogs were in the sample and how many of those were marked. You also know the total number of marked hedgehogs.
Set up a proportion.
marked hedgehogs counted / total hedgehogs counted = total marked hedgehogs / estimated hedgehog population
Plug in the numbers you know and solve for the hedgehog population, p.
23/1000 = 69/p
23/1000 ( 1000p ) = 69/p ( 1000p ) Multiply both sides by 1,000p
23p = 69 · 1,000 Simplify
23p = 69,000 Simplify
p = 3,000 Divide both sides by 23
The best estimate for the hedgehog population is 3,000.
let’s practice! 🖊️
