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Collecting, representing and interpreting data (Single-variable data…

- - - - Pros
        
        Highlights outliers
        
        Makes it easy to compare data sets
      - Cons
        
        Data is grouped into only four categories so some detailed analysis is not possible
    - - Pros
        
        Clearly shows shape of distribution
      - Cons
        
        Doesn't always highlight outliers
        
        It is possible but not easy to estimate Q1, Q2 and Q3
    - - Pros
        
        Makes it easy to find the number summary five
      - Cons
        
        Doesn't always highlight outliers
        
        If interval boundaries are not shown the degree of detail is not clear
- - - - Simple random sampling- every member of th population is equally likely to be chosen. For example, allocate each member of the population a number. Then use random numbers to choose a sample of the desired size
      - Systematic sampling- find a sample of size n from a population of size N by taking one member from the first k members of the population at random and then selecting every kth member after that, where k = N/n
      - Stratified sampling- when you know you want distinct groups to be represented in your sample, split the population into these distinct groups and then sample within each group in proportion to its size
    - - Opportunity sampling- Taking samples from members of the population you have access to until you have a sample of the desired size
      - Quota sampling- when you know you want distinct groups to be represented in your sample, decide how many members of each group you wish to sample in advance and use opportunity sampling until you have a large enough sample for each group
      - Cluster sampling- split the population into clusters that you expect to be similar to each other, then take a sample from each of these clusters
- - - - The median of a set of data is the middle value of data listed in order of size
    - - To work out the mean x̄ of a set of n observations, calculate their sum and divide the result by n x̄ = Σx/n
        The mean of a set of data given in the form of a frequency distribution is given by x̄ = Σfx/Σf
    - - The mode of a set of data is the value or category that occurs most often or has the largest frequency. For grouped data, the modal interview or modal group is normally given
  - - - Interquartile range
        
        Q1: (n+1)/4
        
        Q3: 3(n+1)/4
        
        The interquartile range (IQR) = Q3 - Q1
      - Variance- measures how spread-out the values are from the mean
        
        The population variance of n observations with mean x̄ is defined as
        σ² = Σ(x-x̄)²/n = Σx²/n - x̄²
      - Range
        
        The range of a set of data is the largest value minus the smallest value
      - Standard deviation- the square roof of the variance √
        
        The population standard deviation of n values with mean x̄ is defined as
        σ = √(Σ(x-x̄)²/n) = √(Σx²/n - x̄²)
  - - - Mode
        
        Pros
        
        Not usually affected by outliers
        
        Not usually affected by errors or omissions
        
        Useful for non-numerical data
        
        Is always an observed data point
        
        Cons
        
        May not be representative if it has a low frequency
        
        There may be other values with similar frequency
        
        Doesn't use all the dat
      - Median
        
        Pros
        
        Not affected by outliers
        
        Not significantly affected by errors
        
        Cons
        
        Doesn't make use of all of the data
      - Mean
        
        Pros
        
        When the data set is very large a few extreme errors have negligible impact
        
        Cons
        
        When the data set is small a few extreme values or values have a big impact
    - - Range
        
        Pros
        
        Reflects the full data set
        
        Cons
        
        Distorted by outliers
      - IQR
        
        Pros
        
        Not distorted by outliers
        
        Cons
        
        Does not reflect all of the data
      - Standard deviation
        
        Pros
        
        When the data set is very large a few outliers have negligible impact
        
        Cons
        
        When the data set is small a few outliers have a big impact
- - - - Positive correlation- the variables increase together
      - Negative correlation- one variable increases as the other decreases
      - Zero correlation- the variables are uncorrelated
    - - For no correlation, r = 0
      - For perfect negative correlation, r = -1
      - For perfect positive correlations, r = 1