Distributions

Understanding Distributions

  • A distribution represents the set of all possible values or intervals of values for a variable and how often they occur.
  • Distributions can be described or summarised by central tendency (mean, mode, median), spread (range, variance, standard deviation), and shape (symmetry, skewness, kurtosis).

Types of Distributions

  • Uniform Distribution: In a uniform distribution, all values have an equal chance of occurring, and the probabilities are uniformly distributed.
  • Normal Distribution: The normal or Gaussian distribution is a bell-shaped and symmetric distribution. The mean, median and mode of a normal distribution are all at the centre.
  • Binomial Distribution: A binomial distribution has two possible outcomes, success or failure. It is used when we have a fixed number of trials each with the same probability of success.
  • Poisson Distribution: The Poisson distribution is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval.

Histograms and Distributions

  • A histogram is used to graphically demonstrate the shape of the distribution. It indicates the frequency of data points within certain ranges.
  • The x-axis represents the variable under inspection, while the height of the bars represents the frequency of the data.
  • The shape of a histogram can indicate whether the distribution is normal, skewed right or left, or if it has any outliers.

Understanding Skewness

  • Skewness measures the asymmetry of a probability distribution.
  • If the distribution is symmetrical, skewness is zero.
  • A positive skew indicates that the tail on the right side is longer or fatter than on the left side. Conversely, a negative skew indicates the tail on the left side is longer or fatter than on the right side.

Importance of Understanding Distributions

  • Knowing the type of distribution allows researchers to apply the appropriate statistical tests and make valid conclusions.
  • Recognising the distribution shape helps in understanding the data, formulating hypotheses and in extrapolation for prediction purposes.
  • Professional fields such as finance, economics, psychology, social sciences, health sciences, and others make use of data distributions for modelling and forecasting.