Statistics · Topic 3 of 13
Statistical Diagrams
Theory
Once data has been classified and gathered, we use statistical diagrams to visualise it. The type of diagram you choose depends entirely on the type of data (categorical or numerical) you are analysing.
1. Diagrams for Categorical Data
- Tables (Frequency & Contingency): Frequency tables show the totals for a single category. Contingency (two-way) tables show how two categorical variables interact. Tables can display raw counts or proportions/percentages.
- Bar Charts: Generated from frequency tables. They use rectangular bars to make clear comparisons between the totals of different categories.
- Pie Charts: A circular chart divided into slices. These are best used when you want to compare the proportions (or percentages) of different categories relative to the whole.
2. Diagrams for Numerical Data
- Histograms: Used to visualise the shape and distribution of a single continuous numerical variable (e.g., to see if data is normally distributed or skewed).
- Boxplots: Provide a visual representation of the five-figure summary.
- The line in the middle of the box is the median.
- The width of the box is the interquartile range (IQR).
- Circles or asterisks outside the whiskers represent outliers.
- Comparative boxplots are excellent for comparing two different numerical datasets side-by-side.
- Scatterplots: Used to present bivariate data (data with two related numerical variables) to visualise relationships and correlations.
- When plotting "Y on X", the independent variable goes on the x-axis, and the dependent variable goes on the y-axis.
Important Exam/Project Rule:
All statistical diagrams must include a clear, descriptive main title and appropriate axis labels to be awarded marks.
Worked examples
Example 1
Example 1: Diagram Selection (Categorical)
A school cafeteria manager has recorded the meal choices (Pasta, Pizza, Salad, or Curry) of 300 pupils. They want to create a visual display specifically to show the proportion of the total pupils that chose each meal. State the most appropriate statistical diagram for this purpose.
A pie chart.
(Pie charts are the best diagram for displaying proportions of categorical data).
Example 2
Example 2: Comparing Boxplots (Numerical)
A manager at a call centre compares the time taken (in seconds) for employees to answer the phone at two different offices, Office A and Office B.
- Office A has a median answer time of 45 seconds and an interquartile range (IQR) of 12 seconds.
- Office B has a median answer time of 38 seconds and an interquartile range (IQR) of 20 seconds.
Make two valid comparisons about the call answering times at the two offices.
Comparison 1 (Location):
On average, the call answering time at Office B is faster because its median (38 seconds) is lower than Office A's median (45 seconds).
Comparison 2 (Spread):
The call answering times at Office A are more consistent because its interquartile range (12 seconds) is smaller than Office B's interquartile range (20 seconds).
Example 3
Example 3: Scatterplots & Bivariate Data
A botanist is investigating how the number of hours of daily sunlight affects the height of a specific type of sunflower.
- (a) State which variable is the independent variable and should be plotted on the x-axis.
- (b) State the name of the statistical diagram that should be used to visualise the relationship between these two variables.
(a) The independent variable is the hours of daily sunlight (because the plant's height depends on the sunlight, not the other way around).
(b) A scatterplot.
Example 4
Example 4: Distributions vs Summaries
A marine biologist has collected data on the weights of 500 adult penguins. They want to check if the data is symmetrically distributed or if it has a skewed shape. Explain whether a boxplot or a histogram would be the most appropriate diagram for this specific task.
A histogram is the most appropriate diagram.
While a boxplot shows the median and spread, a histogram is much better at clearly visualising the overall shape and distribution of a single numerical dataset.