Chapter 3 - Summarising Data

• Weighted mean

  sum of (weight x value)/ sum of weights
• Geometric mean

  nth square root ( value1 x value2 x ... x value n)
• Mode

  Advantages : easy to use, always a value in the data, unaffected by outliers, can be used with qualitative and quantitative

  Disadvantages : may not be one, or may be more than one, cannot be used to calculate measures of spread, not always representative
• Median

  Advantages : easy to find when data is in order, unaffected by outliers, best to use with skewed data, can be used to calculate quarterlies, IQR and skew

  Disadvantages : may not be data value, not always representative of data
• Mean

  Advantages : uses all data, can be used to calculate sd and skew

  Disadvantages : may not be data value, affected by outliers
• Quartiles

  Discrete data :

  LQ = 1/4 x (n+1)th value

  UQ = 3/4 x (n+1)th value

  Grouped data :

  LQ = 1/4 nth value

  UQ = 3/4 nth value
• Outliers

  > UQ + (1.5 x IQR)

  < LQ + (1.5 x IQR)

  values outisde mean + (3 x standard deviation)
• Skewness

  Positive skew : mean>median>mode

  Negative skew : mean<median>mode

  Symmetrical : mean = median = mode

  Skewness = 3(mean-median)/ standard deviation
• Comparing data sets

  • measure of average
  • measure of spread
  • skew