GCSE Statistics Verified Solutions

GCSE Statistics Verified Solutions Population ️️A collection of all the items Sample ️️A selection of the population to use data from Census ️️When data is taken from every member in the population Advantages of a census over a sample ️️More representative, less biased, includes everyone's opinions Advantages of a sample over a census ️️Quicker, cheaper, easier to analyse as less data Disadvantages of a census over a sample ️️Time consuming, expensive, difficult to do Disadvantages of a sample over a census ️️Less representative, possibly biased Pilot Study ️️A small scale replica of the survey to be carried out. Advantages of a pilot study ️️Ensures questions can be understood, identify ambiguity, test response rate, identifies likely responses, check methods Sampling Frame ️️A list containing data that a sample can be taken from Examples of a sampling frame ️️Electoral role, SIMS register, DVLA, telephone directory Primary Data ️️Data that has been collected by the person doing the survey Secondary data ️️Data that hasn't been collected by the person doing the survey Advantages of primary data ️️More reliable, up-to-date, tailored for investigation Advantages of secondary data ️️Easier to obtain, cheaper, less time-consuming Continuous Data ️️Data that lies on a continuous scale (can be at any point on a number line) Discrete Data ️️Data that consists of separate numbers (jumps along the number line) Quantitative Data ️️Data that has numerical values Qualitative Data ️️Data that is not numerical values Open Questions ️️Has no suggested answers and has freeform boxes to reply in Advantages of open questions ️️Allows for a range of responses, so can cover all eventualities Closed Questions ️️Has a set of answers for the person to choose from Advantages of closed questions ️️Easier to analyse as range of responses restricted Leading Questions ️️Questions that infer an opinion and promote a certain answer Convenience Sample ️️The first so many pieces of data in the list are sampled Advantages of a convenience sample ️️Quick and easy Disadvantages of a convenience sample ️️Unlikely to be representative Random Sample ️️Each person has an equally likely chance to be picked How to take a random sample ️️(a) Number everyone in list (b) Use a random number generator to select numbers (c) Select the data points corresponding to the numbers picked (d) If you get a number outside the range or the same number twice you repeat, if you get a decimal round to the nearest number. Advantages of a random sample ️️Easy to do Disadvantages of a random sample ️️May not be representative Systematic Sample ️️Data is chosen at regular intervals (e.g. every 10th person) How to take a systematic sample ️️Order population and divide population by sample size to find how often data chosen. Then choose random number to decide where in this interval to start. Advantages of a systematic sample ️️Useful for production line - will spot problems over time Disadvantages of a systematic sample ️️May not be representative Quota Sample ️️The same amount of people from different chosen groups are sampled How to take a quota sample ️️Decide on a quota size for each group. Then take a random sample, ignoring any results from a group where the quota has been reached. Advantages of a quota sample ️️Makes sure all quota groups are represented, easy to take Disadvantages of a quota sample ️️Not likely to be representative, may be difficult to reach quota if numbers limited Cluster Sample ️️The population is divided into groups and a group is chosen at random. Advantages of a cluster sample ️️Easy to do Disadvantages of a cluster sample ️️Unlikely to be representative Stratified Sample ️️Where the data sampled in each group is proportional to that of the whole population How to take a stratified sample ️️Multiply the fraction of each group in the whole population by the total sample size to decide on the size of the sample in each strata. Then take a random sample. Advantages of a stratified sample ️️Representative Disadvantages of a stratified sample ️️Harder to collect, more expensive Features of a good question ️️Unambiguous, closed, non-overlapping answer boxes, unbiased/not leading, not offensive or personal, easy to analyse Positive correlation ️️As one variable increases, so does the other Negative correlation ️️As one variable increases, the other decreases Response variable ️️The variable being measured or studied