Displaying Data and Frequency Distributions

Purpose of Data Visualisation

  • Generates actionable insight from raw data.

  • Uncovers underlying data structures and distributions.

  • Identifies key variables of interest.

  • Detects data entry errors, anomalies, and outliers.

  • Clarifies patterns that are difficult to discern in tabular form.

Frequency Distributions

  • Frequency Distribution Table: A structured summary showing the number of observations within each distinct category.

  • Absolute Frequency: The raw count of occurrences within a specific category.

  • Relative Frequency: The proportion or percentage of the total dataset represented by a category:   Relative Frequency=Absolute FrequencyN×100\text{Relative Frequency} = \frac{\text{Absolute Frequency}}{N} \times 100

  • Cumulative Frequency: The progressive running sum of absolute frequencies through successive categories.

  • Cumulative Relative Frequency: The progressive running sum of relative percentages, terminating at 100.00%100.00\%.

Bar Charts

  • Used to display categorical or discrete variables.

  • Categories are positioned along one axis, with bar height representing absolute or relative frequency.

  • Sorting categories by frequency (from highest to lowest) substantially improves readability and quick comparison.

Crime counts reordered by frequency

Histograms

  • Used for continuous numerical data divided into intervals (bins).

  • Contiguous vertical bars represent frequencies across numeric intervals with no gaps between bars.

  • Enables rapid detection of:

    • The mode (peak frequency interval).

    • Shape and skewness of the distribution.

    • Data anomalies and extreme outliers across subsets.

Distribution of violent crime counts across Brisbane neighbourhoods

Line Charts

  • Optimal for tracking trends, rates, and continuous changes over time.

  • Positions sequential time periods on the horizontal axis and metric rates along the vertical axis.

  • Facilitates comparison of multiple series simultaneously (such as male versus female imprisonment rates over time).

Selecting Appropriate Charts

  • Comparison:

    • Few items or periods: Bar charts or column charts.

    • Over time / many periods: Line charts.

  • Distribution:

    • Single variable (continuous): Histograms.

    • Multiple variables: Scatter plots.

  • Composition:

    • Static share of total: Pie charts or waterfall charts.

    • Changes over time: Stacked column charts or stacked area charts.

  • Relationship:

    • Two variables: Scatter charts.

    • Three variables: Bubble charts.

Chart Chooser guide by Andrew V. Abela