Classifying Data
The first step in any analysis is to correctly classify variables. This determines the graphs and statistics you can use. Test your knowledge below.
Categorical Data
Represents qualities or labels.
- Nominal: Categories with no order (e.g., Type of car).
- Ordinal: Categories with a natural order (e.g., T-shirt size S, M, L).
Numerical Data
Represents quantities that are counted or measured.
- Discrete: Counted values (e.g., Number of pets).
- Continuous: Measured values (e.g., Height in cm).
Check Your Understanding
Summarising Numerical Data
We use statistics to summarise the centre and spread of data. For symmetrical data, we use the mean and standard deviation. For skewed data, we use the median and interquartile range (IQR). Use the calculator below to explore these measures.
Measures of Centre
Mean ($\bar{x}$): —
Median (M): —
Measures of Spread
Range: —
Interquartile Range (IQR): —
Standard Deviation (s): —
Boxplots & The Five-Number Summary
A boxplot visually represents the five-number summary and helps identify outliers. An outlier is any data point that falls outside the “fences” calculated using the 1.5 x IQR rule.
The Five-Number Summary
- Minimum Value
- First Quartile (Q1)
- Median
- Third Quartile (Q3)
- Maximum Value
Outlier Fences
- Lower Fence: Q1 – 1.5 × IQR
- Upper Fence: Q3 + 1.5 × IQR
Interpreting a Boxplot
Each of the four sections of a boxplot (the two whiskers and the two halves of the box) contains 25% of the data points, regardless of its visual length.
Scatterplots & Association
To investigate the relationship between two numerical variables, we use a scatterplot. We describe the association by commenting on its direction, form, and strength.
Select an association type to view an example.
Correlation vs. Causation
A strong correlation between two variables does not automatically mean one causes the other. It’s a critical error to assume causation from correlation alone. There may be other explanations.
Modelling with Least Squares Regression
When a scatterplot shows a linear association, we can model it with a least squares regression line. The equation of this line, y = a + bx, can be used to make predictions. The reliability of these predictions depends on whether they are an interpolation or extrapolation.
Model Details
Equation: y = 1.87x + 10.5
Correlation (r): 0.95
Coefficient of Determination (rยฒ): 0.90
This means 90% of the variation in the response variable can be explained by the variation in the explanatory variable.
