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A Level Maths > Statistics > Flashcards

Statistics Flashcards

1
Q

what is a population?

A

the whole set of items that are of interest.

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2
Q

what is a sample?

A

some subset of the population intended to represent the population.

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3
Q

what is a sampling unit?

A

each individual thing in the population that can be sampled.

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4
Q

what is a sampling frame?

A

sampling units of a population are individually named or numbered to form a list.

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5
Q

what is a census?

A

observes or measures every member of a population (gathering information from every person in the population).

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6
Q

what are the advantages of a census?

A

it should give a completely accurate result.

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7
Q

what are the disadvantages of a census?

A
  • time consuming and expensive.
  • cannot be used when the testing process destroys the item.
  • hard to process large quantity of data.
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8
Q

what are the advantages of a sample?

A
  • less time consuming and expensive than a census.
  • fewer people have to respond.
  • less data to process than in a census.
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9
Q

what are the disadvantages of a sample?

A
  • the data may not be as accurate.
  • the sample may not be large enough to give information about small sub-groups of the population.
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10
Q

what are the 3 methods of random sampling?

A

simple random sampling, systematic sampling and stratified sampling.

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11
Q

what is simple random sampling?

A

every sample has an equal chance of being selected.

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12
Q

what is the method of simple random sampling?

A

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).

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13
Q

what are the advantages of simple random sampling?

A
  • free of bias.
  • easy and cheap for small populations and small samples.
  • each sampling unit has an equal chance of selection.
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14
Q

what are the disadvantages of simple random sampling?

A
  • not suitable for large population / sample size as it is time consuming, disruptive and expensive.
  • a sampling frame is needed.
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15
Q

what is systematic sampling?

A

the required elements are chosen at regular intervals from an ordered list.

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16
Q

what is the method of systematic sampling?

A

a sampling frame is needed, the first person or thing is chosen at random then the next people / items are chosen in intervals.

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17
Q

what are the advantages of systematic sampling?

A
  • simple and quick to use.
  • suitable for large samples and large populations.
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18
Q

what are the disadvantages of systematic sampling?

A
  • sampling frame is needed.
  • can introduce bias if the sampling frame is not random.
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19
Q

what is stratified sampling?

A

the population is divided into mutually exclusive strata and a random sample is taken from each.

20
Q

what is the method of stratified sampling (the formula)?

A

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

21
Q

what are the advantages of stratified sampling?

A
  • the sample accurately reflects the population structure.
  • guarantees proportional representation of groups within a population.
22
Q

what are the disadvantages of stratified sampling?

A
  • the population must be clearly classified into distinct strata.
  • selection within each stratum is not suitable when population is large.
23
Q

what are the 2 types of non-random sampling?

A

quota sampling and opportunity/convenience sampling.

24
Q

what is quota sampling?

A

when an interviewer or researcher selects a sample that reflects the characteristics of the whole population.

25
Q

what is the method of quota sampling?

A

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.

26
Q

what are the advantages of quota sampling?

A
  • 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.
27
Q

what are the disadvantages of quota sampling?

A
  • can introduce bias.
  • population must be divided into groups which can be costly or inaccurate.
  • time consuming and expensive.
  • non-responses are not recorded.
28
Q

what is opportunity / convenience sampling?

A

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.

29
Q

what is the method of opportunity / convenience sampling (example)?

A

an example would be going outside the football stadium asking people their favourite sports.

30
Q

what are the advantages of opportunity / convenience sampling?

A
  • easy to carry out.
  • inexpensive.
31
Q

what are the disadvantages of opportunity / convenience sampling?

A
  • unlikely to provide a representative sample.
  • highly dependent on individual researcher.
32
Q

what is quantitative variables / data?

A

variables or data associated with numerical observations.

33
Q

what is qualitative variables / data?

A

variables or data associated with non-numerical observations.

34
Q

what is a continuous variable?

A

a variable that can take any value in a given range.

35
Q

what is a discrete variable?

A

a variable that can take only specific values in a given range.

36
Q

in a grouped frequency table, what do the class boundaries tell us?

A

the maximum and minimum values that belong in each class.

37
Q

in a grouped frequency table, what does the midpoint tell us?

A

average of class boundaries.

38
Q

in a grouped frequency table, what does the class width tell us?

A

the difference between upper and lower class boundaries.

39
Q

what are measures of location?

A

single values which describe a position in a data set.

40
Q

what are measures of central tendency?

A

single values which describe the centre of the data, i.e. notion of average.

41
Q

what are the measures of central tendency used in maths?

A

mean, median and mode/modal class.

42
Q

what is the mean?

A

it is …. and it can be calculated using the formula

43
Q

what is the median?

A
44
Q

what is the mode/modal class?

A
45
Q

how do you find the position of the median for listed discrete data?

A

find n/2
- if a decimal, round up
- if whole use halfway between this item and one after.

46
Q

how do you find the position of the median for grouped continuous data?

A

find n/2, then use linear interpolation.

A Level Maths (3 decks)

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