Population and sampling for OCR GCSE Maths

1. Sampling data
2. Populations

When surveys are carried out, every single person/object that is relevant cannot be realistically asked/checked. The set of all the people/objects relevant to a survey is called the population. To combat this issue, a sample is taken. A sample is a subset of the population to be used in the survey and a sampling unit is each element of the sample. Sampling is a lot easier to carry out rather than asking every element of the population and is thus less time-consuming and a lot cheaper. Since a sample represents the population it is taken from, it also gives accurate results. Also, in cases of limited resources, sampling is ideal since it doesn't use up the whole population. However, there is still a chance of bias and there are difficulties in selecting a truly representative sample.

The population of a survey is every person/object that is asked/checked during a survey. Using the entire population means that everyone's opinion is accounted for, meaning that the results are free from bias and are more reliable. However, asking the whole population could be extremely time-consuming and costly.

1

A bakery wants to conduct a survey about the bread buying habits of its customers. The bakery asks every customer that visits them on a random day. Explain whether the bakery has asked the whole population or has taken a sample.

The population of this survey is all of the bakery's customers. It is most likely that the bakery was not visited by every single one of its customers on any random day, thus the whole population cannot have been asked in one random day. Therefore, the bakery has taken a sample.

Sample as not all customers have visited the bakery on that day.

2

A student wants to carry out a survey about stress levels at school. On Monday, he asks 20 students leaving school to rate their stress levels from 1 to 10. State what is the sample of the survey.

The student's sample is the 20 students he asks.

20 students

3

A teacher wants to carry out a survey for her class of 25 students to deduce what they think about the amount of homework they receive. Explain if she should use a sample or the whole population.

Since the population is relatively small, the teacher could use the whole population instead of a sample. This will account for every student's opinion and the results will be free from bias and reliable.

the whole population due to the size of it

4

A city of population 100000 is trying to collect information about its population's public transport habits. Explain why using a sample may be a better idea than using the whole population.

Asking the whole population of 100000 people will be time-consuming and expensive, so using a sample may be a better idea since it will eliminate these problems.

fewer people interviewed → less time-consuming

5

Explain why manufacturing companies cannot use the whole population during quality checks.

For specific types of products, using the products will use them up or damage them. If a manufacturing company were to conduct quality check on every product they manufactured, it would destroy its entire supply.