Standardisation and Petersen Capture-Recapture

Estimating what you cannot count

You cannot line up every fish in a lake to count them, but statistics lets you estimate the total from a sample. This module covers two Higher-tier tools: the capture-recapture method for estimating a population, and standardisation for comparing a value against the average. It also looks at why a bigger sample gives a more reliable answer.

Estimation vocabulary

Learn these four terms before you study the methods.

Two different tools

The two methods answer different questions.

Learn the formula, check the rules

These are Higher-tier tools. The capture-recapture formula must be memorised: multiply the two sample sizes together, then divide by how many marked ones turn up in the second catch. It only works if the population stays closed and the marks do not wear off or change survival. Standardisation takes a value, takes away the mean and divides by the spread. Remember a larger sample gives a more reliable estimate.

Match the term

The capture-recapture formula

How do you estimate the population with the capture-recapture formula?

• Multiply the two samples, then divide by the number marked in the second.
• Add the two samples together.
• Subtract the marked ones from the first sample.
• Take the mean of the two samples.

Assumptions

Select the TWO assumptions the capture-recapture method relies on.

• The population stays closed, with no births or migration.
• The marks do not wear off or change survival.
• Every animal is counted directly.
• Only one sample is ever taken.

Order the method

Put the steps of the capture-recapture method in order, earliest first.

• Catch a first sample
• Mark them and release them
• Catch a second sample later
• Count how many are marked
• Put the numbers into the formula

Complete the facts

The whole group being studied is the _____. A smaller part of it is a _____. To estimate a population you cannot count, use _____. Its formula multiplies the two samples and divides by the number _____ in the second sample. To standardise a value you subtract the mean and divide by the standard _____.

Estimate the population

A first sample of 20 fish is marked and released. A second sample of 30 fish is caught, and 6 of them are marked. Multiply 20 by 30, then divide by 6, to estimate the population. What is the answer?

Standardise a value

A value is 70, the mean is 60 and the standard deviation is 5. Subtract 60 from 70 to get 10, then divide 10 by 5 to standardise it. What is the answer?

True of sample size

Tap the TWO statements that are true about sample size.

• a larger sample gives a more reliable estimate
• sample means cluster more closely than single values
• a smaller sample is always more reliable
• one person is enough to estimate a whole population

Choose the method

Read each task and choose the right answer.

• A scientist wants to estimate how many deer live in a forest without counting them all. Which method fits?
• You want to compare one test mark against the average, taking the spread into account. Which method fits?
• A survey uses only 5 people to estimate a whole city. What is the main problem?

Explain the methods

Explain how the capture-recapture method estimates a population and how standardisation compares a value.

• State the capture-recapture formula and one assumption it relies on
• Explain how to standardise a value using the mean and standard deviation
• Explain why a larger sample gives a more reliable estimate