Year One

• In statistics, a population is a whole set of items that are of interest.
• A census observes or measures every member of a population.
• A sample is a selection of observations taken from a subset of the population which is used to find out information about the population as a whole.
• One disadvantage of a census is that they can be time-consuming and expensive.
• One disadvantage of a census is that it can be hard to process large quantities of data.
• One advantage of a sample is that they are less time consuming and expensive than a census.
• One advantage of a sample is that fewer people have to respond.
• One advantage of a sample is that there is less data to process than a census.
• One disadvantage of using a sample is that the data may not be as accurate.
• Sampling units are individual units of the population.
• A sampling frame is a list of individually named/numbered sampling units of a population.
• In random sampling, every member of the population has an equal chance of being selected, hence the sample should be representative.
• Random sampling helps remove bias from a sample.
• A simple random sample of size n is one where every sample of size n has an equal chance of being selected.
• In systematic sampling, the required elements are chosen at regular intervals from an ordered list.
• In stratified sampling, the population is divided into mutually exclusive strata (males and females, for example) and a random sample is taken from each. The proportion of each strata sampled should be the same.
• One advantage of simple random sampling is that it is free of bias. Also, it is cheap and easy to implement for small populations and small samples. Finally, each sampling unit has a known and equal chance of selection.
• One disadvantage of simple random sampling is that it isn't suitable for extremely large population sizes or sample sizes as it can be time consuming, disruptive and expensive. Also, a sampling frame is needed.
• One advantage of systematic sampling is that it is simple and quick to use. Also, it is suitable for large samples and large populations.
• One disadvantage of systematic sampling is that a sampling frame is needed. Also, it can introduce bias if the sampling frame is not random.
• One advantage of stratified sampling is that the sample accurately reflects the population structure. Also, it guarantees proportional representation of groups within a population.
• One disadvantage of stratified sampling is that the population must be clearly classified into distinct strata. Also, selections within each stratum suffers from the same disadvantages as the simple random sampling method.
• In quota sampling, an interviewer or researcher selects a sample that reflects the characteristics of the whole population.
• Quota sampling occurs when the population is divided into groups based on a certain characteristic. The size of each group determines the proportion of the sample with that characteristic. Interviewers meet people, assess their group, and then post-interview will allocate them into the right quota. This continues until all quotas are filled.
• Opportunity sampling consists of taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking for.
• One advantage of quota sampling is that it allows a small sample to still be representative of the population. Also, no sampling frame is required and it is quick, easy and inexpensive. Finally, it allows for easy comparison between different groups within a population.
• One disadvantage of quota sampling is that non-random sampling can introduce bias. Also, the population must be divided into groups, which can be costly and inaccurate. Increasing scope of study can also increase the number of groups, which adds time and expense. Finally, non-responses are not recorded as such.
• One advantage of opportunity sampling is that it easy to carry out and inexpensive.
• One disadvantage of opportunity sampling is that it is unlikely to provide a representative sample. Also, it is highly dependent on the individual researcher.
• Variables or data associated with numerical observations are called quantitative variables/data. For example, shoe size is quantitative.
• Variables or data associated with non-numerical observations are called qualitative variables/data. For example, hair colour is qualitative.
• A variable that can take any value in a given range is a continuous variable. For example, time can take any value.
• A variable that can only take specific values in a given range is a discrete variable. For example, the number of people in a family can only be a whole number.
• The midpoint is the average of the class boundaries.
• When data is presented as a grouped frequency table, the specific data values are not shown. The groups are more commonly known as classes.
• Class boundaries tell you the maximum and minimum values that belong in each class.
• The class width is the difference between the upper and lower class boundaries.
• A random variable is variable whose value depends on the outcome of a random event.
• The range of values that a random variable can take is called the sample space.
• A probability distribution describes fully the probability of any outcome in the sample space.