Statistics Flashcards
what is a population?
the whole set of items that are of interest.
what is a sample?
some subset of the population intended to represent the population.
what is a sampling unit?
each individual thing in the population that can be sampled.
what is a sampling frame?
sampling units of a population are individually named or numbered to form a list.
what is a census?
observes or measures every member of a population (gathering information from every person in the population).
what are the advantages of a census?
it should give a completely accurate result.
what are the disadvantages of a census?
- time consuming and expensive.
- cannot be used when the testing process destroys the item.
- hard to process large quantity of data.
what are the advantages of a sample?
- less time consuming and expensive than a census.
- fewer people have to respond.
- less data to process than in a census.
what are the disadvantages of a sample?
- the data may not be as accurate.
- the sample may not be large enough to give information about small sub-groups of the population.
what are the 3 methods of random sampling?
simple random sampling, systematic sampling and stratified sampling.
what is simple random sampling?
every sample has an equal chance of being selected.
what is the method of simple random sampling?
a sampling frame is needed, each person or thing is given a unique number and a selection of these numbers are chosen at random - done through generating random numbers or lottery sampling (written on tickets and placed in a hat).
what are the advantages of simple random sampling?
- free of bias.
- easy and cheap for small populations and small samples.
- each sampling unit has an equal chance of selection.
what are the disadvantages of simple random sampling?
- not suitable for large population / sample size as it is time consuming, disruptive and expensive.
- a sampling frame is needed.
what is systematic sampling?
the required elements are chosen at regular intervals from an ordered list.
what is the method of systematic sampling?
a sampling frame is needed, the first person or thing is chosen at random then the next people / items are chosen in intervals.
what are the advantages of systematic sampling?
- simple and quick to use.
- suitable for large samples and large populations.
what are the disadvantages of systematic sampling?
- sampling frame is needed.
- can introduce bias if the sampling frame is not random.
what is stratified sampling?
the population is divided into mutually exclusive strata and a random sample is taken from each.
what is the method of stratified sampling (the formula)?
the proportion of each strata sample should be equal, the formula is:
number sampled in a stratum = (number in stratum / number in population) x overall sample size
what are the advantages of stratified sampling?
- the sample accurately reflects the population structure.
- guarantees proportional representation of groups within a population.
what are the disadvantages of stratified sampling?
- the population must be clearly classified into distinct strata.
- selection within each stratum is not suitable when population is large.
what are the 2 types of non-random sampling?
quota sampling and opportunity/convenience sampling.
what is quota sampling?
when an interviewer or researcher selects a sample that reflects the characteristics of the whole population.
what is the method of quota sampling?
the population is divided into groups according to a given characteristics, the size of each group determines the proportion of the sample, the interviewer would meet people, assess group and allocate into appropriate quota - this would be continuously until all quotas have been filled.
what are the advantages of quota sampling?
- allows small samples to be representative of population.
- no sampling frame is required.
- quick, easy and inexpensive.
- allows easy comparison between different groups within a population.
what are the disadvantages of quota sampling?
- can introduce bias.
- population must be divided into groups which can be costly or inaccurate.
- time consuming and expensive.
- non-responses are not recorded.
what is opportunity / convenience sampling?
it 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.
what is the method of opportunity / convenience sampling (example)?
an example would be going outside the football stadium asking people their favourite sports.
what are the advantages of opportunity / convenience sampling?
- easy to carry out.
- inexpensive.
what are the disadvantages of opportunity / convenience sampling?
- unlikely to provide a representative sample.
- highly dependent on individual researcher.
what is quantitative variables / data?
variables or data associated with numerical observations.
what is qualitative variables / data?
variables or data associated with non-numerical observations.
what is a continuous variable?
a variable that can take any value in a given range.
what is a discrete variable?
a variable that can take only specific values in a given range.
in a grouped frequency table, what do the class boundaries tell us?
the maximum and minimum values that belong in each class.
in a grouped frequency table, what does the midpoint tell us?
average of class boundaries.
in a grouped frequency table, what does the class width tell us?
the difference between upper and lower class boundaries.
what are measures of location?
single values which describe a position in a data set.
what are measures of central tendency?
single values which describe the centre of the data, i.e. notion of average.
what are the measures of central tendency used in maths?
mean, median and mode/modal class.
what is the mean?
it is …. and it can be calculated using the formula
what is the median?
what is the mode/modal class?
how do you find the position of the median for listed discrete data?
find n/2
- if a decimal, round up
- if whole use halfway between this item and one after.
how do you find the position of the median for grouped continuous data?
find n/2, then use linear interpolation.
