Statistics and Mechanics

    Cards (49)

    • 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
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