Statistics
Statistics - Book 1
1. Data collection
Population: All of the data set that is of interest.
Census: Observes or measures every member of the population.
Sampling units: Individual units of a population.
Sampling frame: A list of individually named or numbered sampling units of a population.
Sample: A selection of observations taken from a subset of the population which is used
to nd out information about a population as a whole.
Advantages Disadvantages
Census • It should give a completely accurate • Time-consuming and expensive
result • Can’t be used when the testing process
destroyed the item
• Hard to process a large quantity of data
Sample • Less time-consuming a expensive • The data may not be as accurate
than a census • The sample may not be large enough to give
• Fewer people have to respond information about small sub-groups of the
• Less data to process than in a census population
Random sampling
Simple random sampling: Every sample of size n has an equal chance of being selected.
Systematic sampling: The required elements are chosen at regular intervals from an
ordered list.
Strati ed sampling: The population is divided into mutually exclusive strata and a random
sample is taken from each.
Advantages Disadvantages
Simple • Free of bias • Not suitable when the population size or the
random • Easy and cheap to implement sample size is large
for small populations • A sampling frame is needed
• Each sampling unit has a known
and equal chance of selection
Systematic • Simple and quick to use • A sampling frame is needed
• Suitable for large samples and • Can introduce bias if the sampling frame is not
large populations random
Strati ed • Sample accurately re ects the • Population myst be clearly classi ed into distinct
population structure strata
• Guarantees proportional • Selection within each stratum su ers from the
representation of groups within a same disadvantages as simple random sampling
population • Is time-consuming
Page 1 of 12 A Level Mathematics
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, Statistics
Non-random sampling
Quota sampling: An interviewer or researcher selects a sample that re ects the
characteristics of the whole population.
Opportunity sampling: Taking the sample from people who are available at the time of the
study and who t the criteria you are looking at.
Advantages Disadvantages
Quota • Allows a small sample to still be • Non-random sampling can introduce bias
representative of the population • Population must be divided into groups,
• No sampling frame required which can be costly or inaccurate
• Quick, easy and inexpensive • Increasing scope of study increases
• Allows for easy comparison between number of groups, adding time and cost
di erent groups within a population • Non-responses are not recorded
Opportunity • Easy to carry out • Unlikely to provide a representative
• Inexpensive sample
• Highly dependant on individual researcher
The large data set
Daily mean temperature in ˚C – this is the average of the hourly temperature readings
during a 24-hour period.
Daily total rainfall including solid precipitation such as snow and hail, which is melted
before being included in any measurements – amounts less than 0.05 mm recorded as ‘tr’
or ‘trace’
Daily total sunshine recorded to the nearest 10th of an hour
Daily mean wind direction and windspeed in knots, averaged over 24 hour from midnight
to midnight. Mean wind directions are given as bearings and as cardinal (compass)
directions. The data from mean windspeed is also categorised according to the Beaufort
scale.
Page 2 of 12 A Level Mathematics
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Statistics - Book 1
1. Data collection
Population: All of the data set that is of interest.
Census: Observes or measures every member of the population.
Sampling units: Individual units of a population.
Sampling frame: A list of individually named or numbered sampling units of a population.
Sample: A selection of observations taken from a subset of the population which is used
to nd out information about a population as a whole.
Advantages Disadvantages
Census • It should give a completely accurate • Time-consuming and expensive
result • Can’t be used when the testing process
destroyed the item
• Hard to process a large quantity of data
Sample • Less time-consuming a expensive • The data may not be as accurate
than a census • The sample may not be large enough to give
• Fewer people have to respond information about small sub-groups of the
• Less data to process than in a census population
Random sampling
Simple random sampling: Every sample of size n has an equal chance of being selected.
Systematic sampling: The required elements are chosen at regular intervals from an
ordered list.
Strati ed sampling: The population is divided into mutually exclusive strata and a random
sample is taken from each.
Advantages Disadvantages
Simple • Free of bias • Not suitable when the population size or the
random • Easy and cheap to implement sample size is large
for small populations • A sampling frame is needed
• Each sampling unit has a known
and equal chance of selection
Systematic • Simple and quick to use • A sampling frame is needed
• Suitable for large samples and • Can introduce bias if the sampling frame is not
large populations random
Strati ed • Sample accurately re ects the • Population myst be clearly classi ed into distinct
population structure strata
• Guarantees proportional • Selection within each stratum su ers from the
representation of groups within a same disadvantages as simple random sampling
population • Is time-consuming
Page 1 of 12 A Level Mathematics
fi fifi fl fffi
, Statistics
Non-random sampling
Quota sampling: An interviewer or researcher selects a sample that re ects the
characteristics of the whole population.
Opportunity sampling: Taking the sample from people who are available at the time of the
study and who t the criteria you are looking at.
Advantages Disadvantages
Quota • Allows a small sample to still be • Non-random sampling can introduce bias
representative of the population • Population must be divided into groups,
• No sampling frame required which can be costly or inaccurate
• Quick, easy and inexpensive • Increasing scope of study increases
• Allows for easy comparison between number of groups, adding time and cost
di erent groups within a population • Non-responses are not recorded
Opportunity • Easy to carry out • Unlikely to provide a representative
• Inexpensive sample
• Highly dependant on individual researcher
The large data set
Daily mean temperature in ˚C – this is the average of the hourly temperature readings
during a 24-hour period.
Daily total rainfall including solid precipitation such as snow and hail, which is melted
before being included in any measurements – amounts less than 0.05 mm recorded as ‘tr’
or ‘trace’
Daily total sunshine recorded to the nearest 10th of an hour
Daily mean wind direction and windspeed in knots, averaged over 24 hour from midnight
to midnight. Mean wind directions are given as bearings and as cardinal (compass)
directions. The data from mean windspeed is also categorised according to the Beaufort
scale.
Page 2 of 12 A Level Mathematics
ff
fi fl
