statistics - year 1

large data set, sampling, [] distributions and []

daily mean temperature

daily mean temperature

• measured in C

• average of the hourly temperature readings measured during a 24-hour period

daily total rainfall

• measured in mm (to 1 d.p.)

• includes rain, snow and hail (melted)

• amounts less than 0.05mm are recorded as ‘tr‘ (trace)

daily total sunshine

• measured in hours (to the nearest tenth of an hour)

daily maximum relative humidity

• the amount of water vapour in the air

• measured as a percentage of maximum water vapour that could be in the air

daily mean windspeed (& direction)

• measured in knots (1 knot = 1.15 mph)

• direction is measured in degrees (to the nearest 10)

daily maximum gust (& direction)

• measured in knots (1 knot = 1.15 mph)*

• direction is measured in degrees (from the north)

*beaufort conversion

daily mean visibility

• the greatest horizontal distance at which an object can be seen in daylight

• measured in dm (decameters/10m)

daily mean pressure

• measured in hectopascals (hPa)

• small range (~980 to 1035)

daily mean cloud cover

• measured in oktas (how many eighths of the sky is covered in clouds)

population

a whole set of items that are of interest

census

observes or measures every member of a population

benefits and drawbacks of a census

• it should give a completely accurate result

• time consuming and expensive

• cannot be used when the testing process destroys the item

sample

• a selection of observations taken from a subset of the population

• used to find out about the population as a whole

benefits and drawbacks of a sample

• less time consuming and expensive than a census

• the data may not be as accurate

• the sample may not be large enough to give accurate information about a small sub-groups of the population

sampling unit

individual units of a population

sampling frame

a list of sampling units that are individually named or numbered

simple random sample

• random sampling method

• each unit is allocated a unique number and numbers are selected randomly

• numbers can be generated randomly (using a computer) or ‘drawn from a hat’

benefits and drawbacks of simple random sampling

• free of bias

• each sampling has a known and equal chance of selection

• not suitable when the population/sample size is large, as it is potentially time consuming, disruptive and expensive

• a sampling frame is needed

systemic sampling

• random sampling method

• required elements are chosen at regular intervals from an ordered list

• the first item is chosen randomly, the rest chosen at regular intervals from the first (e.g. every 5 items)

benefits and drawbacks of systemic sampling

• simple and quick to use

• suitable for large populations/samples

• a sampling frame is needed

• can introduce bias if sampling frame is not random

stratified sampling

• random sampling method

• the population is divided into mutually exclusive strata (e.g under 18s and over 18s) and a simple random sample is taken from each

• the number of samples taken from each strata must be proportional to the population

benefits and drawbacks of stratified sampling

• sample accurately reflects the population structure

• guarantees proportional representation of groups within a population

• population must be clearly classified into distinct strata

• selection within each stratum has the same disadvantages as simple random

quota sampling

• non-random sampling

• the population is divided into groups (quotas) according to a given characteristic

• the interviewer meets people, assesses their group and allocates them into the appropriate quota

benefits and drawbacks of quota sampling

• allows a small sample to still be representative of the population

• no sampling frame required

• quick, easy and inexpensive

• non-random sampling can introduce bias

opportunity sampling

• non-random sampling method

• consists of taking a sample from people who are available at the time, who fit the criteria

benefits and drawbacks of opportunity sampling

• inexpensive and easy to carry out

• unlikely to provide a representative sample

• highly dependent on individual researcher

quantitative data

data associated with numerical observations

qualitative data

data associated with non-numerical observations

continuous variable

a variable that can take any value in a given range

discrete variable

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

frequency density

frequency ÷ class width