Descriptive statistics

• Descriptive statistics are used to describe the main trends in data for conclusions
• Descriptive statistics include

  • Measures of central tendency - mean median mode
  • Measures of dispersion - range and standard deviation
  • Graphical representations of data - bar charts, pie charts, scatter graphs, histograms and frequency distribution
• Measures of central tendency are the value in the group that is most typical
• Mean is adding all the values in a set of data and dividing by the total number of values
• Mean disadvantages

  • Not useful in nominal data
  • Easily disrupted or skewed
• Strengths of mean

  • All the information of data is used
• The median is the central value when the values are in rank order and the middle value is selected
• Median strengths

  • not distorted by extreme results (skewed data)
• Median weaknesses

  • Does not take into account the exact value
  • Less meaningful with small sets of data
  • Not meaningful when used in mutually exclusive categories
• The mode is the most frequently appearing number however data can be bi-modal or multi-modal
• Strengths of the mode

  • Useful for mutually exclusive categories
  • Not influenced by extreme scores in skewed data
• Mode weaknesses

  • Crude measure as its not sensitive to exact values (not great representation)
  • Not useful when there are many modes
  • Easily swayed by small changes
• The range is the distance between the largest and smallest scores in the set of data. Difference between highest and lowest score
• Strengths of range

  • Quick and easy to calculate
• Weaknesses of range

  • Less effective when data is skewed
  • Very little information about the spread
• Standard deviation is a measure on average each of the scores in a data set deviates from the mean
• Strengths of standard deviation are

  • its the most sensitive and powerful meaning it will be very representative / accurate
  • less disrupted/skewed
• Limitations of standard deviation

  • Not quick and easy to calculate
• Standard deviation

  • Calculate mean
  • Take away mean from each value
  • Square the taken away value
  • Add up all those squares
  • Divide by n-1
  • Square root result