Data Handling - Range as a Measure of Spread

Definition of Range: The range is a measure of spread that represents the difference between the greatest and least values in a data set. Visually, if you plot your data points on a number line, the range is the total horizontal distance covered from the first point on the left to the last point on the right.

Measure of Variation: Range tells us how 'spread out' or 'clustered' the data is. A small range indicates that the data values are close to each other, resulting in a narrow cluster on a dot plot. A large range indicates that the data values are widely distributed, appearing as a broad, sparse spread of points.

Identifying Extremes: To calculate the range, you must first identify the maximum (highest value) and the minimum (lowest value). In a stem-and-leaf plot, the minimum is the first entry (top-left) and the maximum is the last entry (bottom-right), provided the plot is ordered.

Impact of Outliers: The range is highly sensitive to outliers, which are values significantly higher or lower than the rest of the data. One extreme outlier can make the range appear very large even if most data points are grouped tightly together. On a graph, an outlier looks like a lone point far away from the main 'body' of data.

Limitations: While the range provides a quick snapshot of the spread, it does not tell us anything about how the data is distributed between the two extremes. For example, two different data sets can have the same range of $20$ even if one is evenly spread and the other is clumped entirely in the middle.

Contextual Interpretation: In real-world data, such as daily temperatures, a range of $2^{\circ}C$ suggests very stable weather, whereas a range of $20^{\circ}C$ suggests significant fluctuation. Visually, a line graph with steep peaks and deep valleys shows a higher range than a flatter line.