Measures of central tendency and dispersion

• Why do we use measures of central tendency of dispersion?

  Raw data can be overwhelming -> lots of numbers without context
• What is the solution to overwhelming raw data?

  Descriptive statistics -> summarising raw qualitative data
• What is included in descriptive statistics?

  • Measures of central tendency
  • Measures of dispersion
  • Graphs
• What are measures of central tendency?

  What we tend to see towards the centre of a data set ('typical' value)

  • Mean
  • Median
  • Mode
• What are measures of dispersion?

  Single values summarising the spread of a data set + the variation between scores

  • Range
  • Standard deviation
• What is the mode?

  The most frequent score in a data set

  • 2 different modes = bimodal (2+ = multimodal)
  • Used for nominal level data

  Pros:

  • Not distorted by outliers
  • Only way of giving average in data categories

  Cons:

  • Small data sets = multiple/no modes = no average value
  • Doesn't include all values in calculation
• What is the median?

  The middle value in a data set ordered from lowest to highest

  • Used for interval level data without outliers + ordinal level data

  Pros:

  • Not distorted by outliers
  • Easy to calculate

  Cons:

  • Doesn't include all values in calculation
  • Even numbers of data sets = median value doesn't exist in raw data
• What is the mean?

  The mathematical average of a data set

  • Used for interval level data (highly objective data)
  • NOT used with ordinal level data -> too subjective

  Pros:

  • Most sensitive method of summarising data

  Cons:

  • Too sensitive for data with outliers -> easily skewed
• What is the range?

  The difference between a data set's highest + lowest values

  • Larger range = larger spread of data

  Pros:

  • Easy to calculate

  Cons:

  • Extreme scores distort value
  • Range doesn't show whether scores cluster around the mean or are evenly spread out
• What is standard deviation?

  A complex calculation using all data points to produce a single value

  • Used when a more specific measure is needed
  • Shows the average distance between each score + the mean -> 1sd = 1 percentile away from the mean

  Pros:

  • Considers all values in its calculation = sensitive
  • Provides info about spread of scores

  Cons:

  • Extreme scores distort sd
  • Difficult to calculate
• Why do we use descriptive statistics?

  They tell us about key aspects of data + allow us to see patterns that we can make inferences/conclusions about the data's meaning from