Selecting the Appropriate Statistical Diagram

Step 1: Identify Your Data Type

Before selecting a diagram, you must classify your data.

• Categorical data is non-numerical data described in words, sorted into groups or labels (e.g., eye colour, favourite car brand).
• Discrete data is numerical data resulting from counting. It can only take specific, separate values (e.g., shoe size, number of siblings).
• Continuous data is numerical data resulting from measurement. It can take any value within a given range, including decimals (e.g., exact height, weight, or time).
• Bivariate data consists of pairs of values for two different variables, used to see if they are connected (e.g., ice cream sales versus daily temperature).

Diagrams for Categorical and Discrete Data

When dealing with categories or counted values, your goal is usually to compare totals or look at fractions of a whole.

• Choose Bar Charts to compare absolute frequency (the number of times a category or value occurs), such as comparing the number of students who travel to school by bus, car, or walking. Bars must be of equal width and separated by gaps.
• Choose Pie Charts to show proportions or "part-to-whole" relationships, such as the market share of different phone brands. They display relative sizes as a sector of a circle, not actual frequencies (unless the total is given).
• Choose Vertical Line Charts for discrete numerical data that has many possible outcomes (e.g., plotting the frequency of specific test scores out of 50), as thick bars would look too cluttered.

To draw a pie chart, calculate the angle for each sector using this formula:

$$\text{Angle} = \frac{\text{Frequency}}{\text{Total Frequency}} \times 360^\circ$$

Diagrams for Continuous Data (Higher Tier)

Continuous data is measured along an unbroken scale, meaning there can be no gaps between the groups.

• Choose Histograms for continuous grouped data, especially when the groups have unequal widths, such as mapping the varying times it takes runners to complete a marathon. Because the scale is continuous, the bars must touch.
• In a histogram, the area of the bar represents the frequency. The vertical axis must always be plotted as frequency density (the frequency per unit of class width).
• Choose Frequency Polygons to compare two continuous distributions. You draw them by plotting and joining the midpoints of where histogram bars would be, allowing you to superimpose two datasets on the same axes (e.g., comparing the distributions of heights for two different sports teams).

Here are the key formulas for working with histograms, using the class width (the difference between the upper and lower boundaries of a group):

$$\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}$$ $$\text{Frequency} = \text{Frequency Density} \times \text{Class Width}$$

Diagrams for Analysing Spread and Retaining Data

Sometimes, you need to understand how spread out the data is, or you need to keep the exact original numbers visible.

• Choose Box Plots to compare the median (the middle value or 50th percentile) and the spread of continuous data, such as comparing the median salaries and income spreads between two different professions.
• Box plots neatly summarise the interquartile range (IQR), which measures the spread of the middle 50% of the data between the lower quartile and the upper quartile.
• Choose Stem and Leaf Diagrams for small-to-medium datasets when you want to show the shape of the distribution while retaining the raw data values, such as recording the exact ages of 30 people in a local club. You must always include a key (e.g., $2 \mid 1$ represents $21$).

Diagrams for Relationships and Trends

When analysing two variables or tracking data over time, you need specialised graphs.

• Choose Scatter Graphs for bivariate data to explore relationships and correlation, such as plotting ice cream sales against daily temperature to spot a positive trend.
• You can draw a line of best fit to make predictions. Interpolation (predicting a value within your existing data range) is generally reliable. Extrapolation (predicting outside your data range) is unreliable.
• Watch out for an outlier (an anomalous point that does not fit the general trend). Also, remember that a strong correlation does not prove causation (that one variable directly causes the other to change).
• Choose Time Series Graphs (line graphs with time on the $x$-axis) for data recorded at intervals to show trends over time, such as plotting a company's monthly profits over five years.