Standard deviation

• Standard deviation:

  • Determines the extent to which data is clustered around the mean > the mean is not reliable as it is influenced by external anomalies
  • Useful if there's two data sets with similar means as there could be very different ranges
  • Small standard deviation = more reliable mean and less variation
  • Large standard deviation = mean is less reliable, more anomalies and greater spread of data
• Standard deviation formula:


  s = standard deviation

  Σ = sum of

  x = each value in data set

  x̄ = mean of all values in data set

  n = number of values in data set

  
  

  Subtract and add the standard deviation result to the mean to find out the result on either side of the mean

  E.g. mean = 78.2 and s = 1.3, so 68% of data lies between 76.9 years and 79.5 years

  
• Example:


  London:

  • The outer boroughs (photo) have a smaller standard deviation which suggests there is less variation in life expectancy in outer boroughs and therefore fewer inequalities/ disparities there. This could be due to:
  • Better air quality
  • Less crime
  • Better housing
  • Richer population