Population and sampling for AQA A-level Maths
This page covers the following topics:
1. Sampling data
3. Sampling techniques
4. Using sampling techniques
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.
There are many sampling techniques in which samples are collected in different ways. Two of these are random sampling and opportunity sampling. In random sampling, each member of the sample has an equal chance of being selected. Each sampling unit is assigned a number and then numbers are randomly generated to pick out the members to include in a sample. Random sampling is easy to carry out and usually lacks bias, however it can prove to be difficult to get a list of the whole population, expensive, time-consuming and can still introduce bias. Opportunity sampling is the process through which a sample is created by using people from the population that are available at the time and are willing to take part. Opportunity sampling is a lot less time consuming than other sampling techniques and is the easiest method to usw, however the results obtained may not be representative of the full population.
Different surveys have different needs and thus it should be considered which sampling technique will give the best results for that specific survey. In some cases where the representation of the population is of high importance, stratified sampling may be used. What stratified sampling does is it separates the population into different strata depending on different qualities of the population. Then, for each stratum, the exact same process as in random sampling takes place. This is often done to ensure that the sample taken is representative of the population of the survey.
Define stratified sampling.
Stratified sampling is when the population is separated into different strata and a random sample is taken from each.
population → strata → random sample
A school is conducting a survey about hours spent studying by students outside of school. They are trying to decide whether to use opportunity sampling or stratified sampling. Explain which would be a better idea.
Different students will be studying different subjects that will require varying hours of study. The school could use stratified sampling instead of opportunity sampling to ensure that students of all branches are represented in their sample and thus they will get more reliable results.
Stratified sampling due to being more representative.
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.
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.
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
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