OCR A-Level Maths

• Population in statistics is the whole set of items that are of interest.
• Information obtained from a population is known as raw data.
• A census measures or observes every member of a population.
• A sample is a selection of observations taken from a subset of population and used to find out more information about the population as a whole.
• Advantages of stratified sampling include accurately reflecting the population structure, providing proportional representation of a group within the population, and requiring a clearly classified population into distinct strata.
• Disadvantages of stratified sampling include the same disadvantages as simple random sampling within each stratum.
• Data collection for stratified sampling involves a cheat sheet for Edexcel Stats/Mech Year 1.
• Advantages of census include results should be completely accurate, but it is time consuming and expensive, cannot be used when testing destroys process, and hard to process large quantity of data.
• Advantages of sample include less time consuming and cheaper, fewer people have to respond, less data needs to be processed, but data may not be as accurate and sample may not be large enough to give information about small subgroups of the population.
• Individual units of a population are known as sampling units.
• Sampling units are named and numbered to form a list called a sampling frame.
• Random sampling ensures each member of the population has an equal chance of being selected, the sample should be representative of the population and bias should be removed.
• There are three types of random sampling: simple random sampling, stratified random sampling, and cluster random sampling.
• Simple random sampling is one where every sample of size has an equal chance of being selected.
• In lottery sampling, the names of members are written on identical cards and placed in a hat, and a sample is drawn.
• Advantages of random sampling include being free of bias, easy and cheap for small samples and populations, each sampling unit has a known and equal chance of selection, but it is not suitable for large samples and populations, and a sampling frame is needed.
• Opportunity sampling or convenience sampling is a type of non-random sampling where a sample is taken from people who are available at the time of study and who fits the criteria you are looking for.
• A factory manager wants to find out about what his workers think about the factory canteen facilities.
• Systematic sampling involves choosing the required elements at regular intervals from an ordered list.
• A variable that can only take specific values is a discrete variable.
• In a grouped frequency table, the specific data values are not shown.
• The workers in each group are numbered.
• In stratified sampling, the number sampled in a stratum is the number in the stratum divided by the number in the population times the overall sample size.
• 48 - 62: 85 workers.
• The total number of workers is 300, with 75 workers in the 18 - 32 age group, 140 workers in the 33 - 47 age group, and 85 workers in the 48 - 62 age group.
• Advantages of quantitative data include its easy and inexpensive nature, but it is unlikely to provide a representative result and is highly dependent on the individual researcher.
• The factory manager can use stratified sampling to select the sample.
• The midpoint is the average of class boundaries.
• Variables associated with numerical observations are called quantitative variables or quantitative data.
• Class boundaries show the maximum and minimum values in each group or class.
• 33 - 47: 140 workers,
• A variable that can take any value in a given range is a continuous variable.
• There are 75 workers between ages 18 and 32, 140 workers between ages 33 and 47, and 85 workers between ages 48 and 62.
• 18 - 32: 75 workers,
• The factory manager decides to give a questionnaire to a sample of 80 workers.
• A random number generator or table is used to produce the required quantity of random numbers.
• The number of workers needed from each age group can be calculated as follows:
• If the number of workers required is not a whole number, it is rounded off to the nearest whole number.
• If you need to do calculations on large data sets in your exam, the relevant extract will be provided.
• The class width is the difference between upper and lower class boundaries.