Measures of central tendency and dispersion

• Descriptive statistics

  The use of graphs, tables and summary statistics to identify trends and analyse sets of data.
• Central tendency

  Mean

  Median

  Mode
• Measures of dispersion

  Range

  Standard deviation
• Evaluation of using the mean

  + Most sensitive as it includes all scores/values in a data set within the calculation, so is more representative of the data as a whole.

  _ Easily distorted by extreme values.
• Evaluation of median

  + Extreme scores do not affect it.

  + Easy to calculate

  _ Less sensitive than the mean as actual values of higher and lower numbers are ignored.
• Evaluation of mode

  _ Crude measure, can be very different to mean and median.

  _ When several modes are in a data collection this is not very useful.

  + Easy to calculate
• Evaluation of the range

  + Easy to calculate.

  _ Only takes into account extreme values which may be unrepresentative of data set as a whole.

  _ Influenced by outliers.

  _ Does not indicate whether most numbers are closely grouped around the mean or are spread out, which standard deviation does.
• Standard deviation

  A measure of dispersion in a set of scores. It tells use by how much, on average each score deviates from the mean.
• What does a large standard deviation value show?

  The greater the dispersion or spread within data set.
• What does a small standard deviation show?

  Low standard deviation reflect the fact that data is tightly clustered around the mean, so all participants responded in a similar way.
• Evaluation of standard deviation

  + More precise, includes all values within final calculation.

  _ Can be distorted by extreme values.