Data analysis: Graphs

• Bar Charts are used for discrete data.

  Key Features:

  • Spaces between bars (to show the data is discrete)
  • X-axis: categories
  • Y-axis: frequency/score

  ✅ Good for nominal or ordinal data
• Histograms are used for continuous data.

  Key Features:

  • No gaps between bars (because data is continuous)
  • X-axis: equal-sized intervals
  • Y-axis: frequency

  ✅ Good for showing distribution of interval or ratio data
• Line Graphs are used for: Showing changes over time or trends in continuous data.

  Key Features:

  • Points plotted and connected by lines
  • X-axis: usually time or another continuous variable
  • Y-axis: score/frequency

  ✅ Shows patterns or trends clearly over time
• Scattergrams are used for correlation data – two continuous variables.

  Key Features:

  • Either of the co-variables occupies the x-axis and the other the y-axis.
  • X and Y axes both show continuous variables.

  Types of correlation:

  • Positive: both increase
  • Negative: one increases, the other decreases
  • Zero: no relationship

  ✅ Only used when looking for relationships, not differences
• Use a bar chart when comparing categories and the data is discrete (nominal/ordinal).
• Use a histogram when there is a distribution of data and the data is continuous (interval/ratio).
• Use a line graph when the data changes over time and is continuous.
• Use a scattergram for correlations where the data is continuous.
• A normal distribution is:

  • A symmetrical, bell-shaped curve
  • Most scores are clustered around the mean
  • The mean = median = mode - all occupy the same mid-point of the curve
  • Equal spread of scores either side
  • The tails of the curve never touch the horizontal x-axis as more extreme scores are possible
• Skewed distributions are asymmetrical distributions — the "tail" drags off to one side. The skew can be positive or negative.
• Positive Skew:

  • Tail is on the right (higher values)
  • Most scores are low on the left side of the graph
  • Mean > Median > Mode
• Negative Skew:

  • Tail is on the left (lower values)
  • Most scores are high
  • Mean < Median < Mode