GCSE(F), GCSE(H),

To avoid **bias** in sampling, a population may be divided into recognisable groups. These divisions create a **stratified sample**.

The first step is to identify the **strata** (or layers) that make up the population. This must be done to reflect any bias that may influence the survey.

Then identify how many will be sampled from each layer. The number of people or items selected from each layer should be in proportion to the number in the layer.

If the size of the population is not know, it can be estimated using the **capture-recapture** method. Use an original sample size of *n*, making sure that each item in the samples identified. The proportion of the original sample to the population can be written as `frac(text(n))(text(N))`.

A second sample takes place of sample size *M*. Identify the items *m*that were included in both samples. Given that the ratio of the samples to the population must be the same:

`frac(text(n))(text(N))` = `frac(text(m))(text(M))` or

N = n x `frac(text( M))(text(m))`

1. A school is conducting a survey about homework. The number of of students in each year is as follows:

Year | Students |
---|---|

7 | 254 |

8 | 264 |

9 | 249 |

10 | 233 |

11 | 214 |

It is intended to survey 250 students using stratified sampling. How many Year 10s should be included in the survey?

Answer: 48

The total number of students at the school is 1214. The number of Year 10s to be surveyed is `frac(250)(1214)` x 233 = 47.98 students, or 48.

2. On a remote Scottish Island, a colony of gulls is being monitored. Last year, 68 gulls were ringed (small rings around their legs). This year, 72 gulls were captured and released, of which 18 had rings from the previous year. What is the estimated population of the colony of gulls, assuming that the population is the same this year as it was last year?

Answer: 272 gulls

Estimated population size N = n x `frac(text( M))(text(m))`

N = `frac((68 xx 72))(18)` = 272

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