Statistics and Mechanics

• Daily Mean Temperature (ºC) to 1.d.p
• Daily Total Rainfall (mm) to 1.d.p
• Daily Total Sunshine (hours) to 1.d.p
• Daily Maximum Relative Humidity (%) - above 95% associated with mist and fog
• Daily Mean Visibility (Dm): 1Dm = 10m
• Daily Mean Total Cloud (oktas)
• Daily Mean Pressure (hPa)
• Daily Mean Windspeed (knots)
• Daily Mean Windspeed (Beaufort conversion) - cumulative
• Daily Maximum Gust (knots)
• Daily Mean Wind Direction (bearing)
• Daily Mean Wind Direction (cardinal direction)
• Daily Maximum Gust Direction (bearing)
• Daily Maximum Gust Direction (cardinal direction) - direction wind is blowing from (eg. direction of 270º (W) means wind is blowing from West to East)
• Rainfall is the only variable with ‘tr’.

  Means values of rainfall less than 0.05mm.

  If using it in a calculation, mean and standard deviation for example, use 0.025 (cleaning data)
• Cloud cover has 9 different outcomes
• Cardinal directions have 16 outcomes
• The only 4 variable to have n/a are daily total sunshine, daily mean windspeed (and Beaufort conversion) and daily maximum gust

  They are n/a for the first 2 weeks of May 1987
• Fmax =μR

  Where μ = the coefficient of friction and R = the reaction force
• Find the Z value in the tables at the back
• X~B(n, p)

  Y~N(np, np(1-p))
• Change data from discrete data to continuous

  P(X = a) - P(a - 0.5 < X < a + 0.5)

  P(X < a) - P(X < a − 0.5)

  P(X > a) - P(X > a + 0.5)

  P(X ≤ a) - P(X ≤ a + 0.5)

  P(X ≥ a) - P(X ≥ a − 0.5)
• For hypothesis testing, H0: ρ=0

  When using the PMCC
• PMCC wants to be further away from 0 than the critical value
• For a random sample of size n take from a random variable X, the sample mean is normally distributed with X~N(μ,((σ^2)/n)).
• Census advantages and disadvantages

  Advantages: Accurate

  Disadvantage: Time consuming, expensive, cannot be used when testing destroys process, hard to process
• Sample advantage and disadvantage

  Advantage: Less time consuming, cheaper, fewer people have to respond, less data needs to be processed

  Disadvantage: Not as accurate, sample may not be large enough to give information about small subgroup of the population
• Census measures or observes every member of a population
• Sample is a selection of observations taken from a subset of the population and used to find out more information about the population as a whole
• Simple random sample of size n is where every sample of size n has an equal chance of being selected
• Simple random sampling advantages ands disadvantages

  Advantages: Unbiased, easy and cheap for small samples, equal chance of being selected

  Disadvantages: Not suitable for large samples, sampling frame needed
• Systematic sampling is where the required elements are chosen at regular intervals from an unordered list
• Systematic sampling advantages and disadvantages

  Advantages: Simple and quick, suitable for large samples

  Disadvantages: Sampling frame needed, bias introduced if sampling frame is not random
• Stratified sampling is where the population is divided into mutually exclusive strata and a random sample is taken from each
• Stratified sampling advantages and disadvantages

  Ad: Accurate of population, proportional representation of groups

  Dis: Population must be clearly classified into distinct strata, not suitable for large samples within the strata, sampling frame needed within strata
• Quota sampling is where a sample is selected from a population based on a set of criteria
• Quota sampling advantages and disadvantages

  Ad: Allows a small sample to represent the whole population, no sampling frame required, quick, easy, inexpensive, easy comparison between different groups within a population

  Dis: Bias, population must be divided into groups - costly or inaccurate, increasing scope of study increases number of groups - increases time and expenses, non-responses not recorded
• Opportunity sampling is where a sample is taken from people who are available at the time of study and fit the criteria needed
• Opportunity sampling advantages and disadvantages

  Ad: easy and inexpensive

  Dis: unlikely to provide a representative result, highly dependant on individual researcher
• Linear Interpolation Formula

  Median = (lower value of the median group) + ([{halfway} - {frequency of the groups before the median}]÷[frequency of median group]) x (width of median group)

  Works for other values, not just the median, just substitute the right numbers