📊 Range, Standard Deviation & IQR
Measures of Spread — SAT Math
Why This Matters: The SAT frequently tests your understanding of how data is spread out. You need to know three key measures: Range, Standard Deviation, and Interquartile Range (IQR). This lesson covers all three with worked examples and strategies.
1. Range — The Simplest Measure of Spread
Definition
$$\text{Range} = \text{Maximum Value} - \text{Minimum Value}$$
The range tells you the total span of your data from smallest to largest. It uses only two values — the extremes.
Example
Data set: $\{4, 7, 2, 9, 15, 3\}$
- Maximum = $15$
- Minimum = $2$
- Range = $15 - 2 = 13$
⚠️ Limitations of Range
Two very different data sets can have the same range:
| Data Set | Range | Distribution |
|---|---|---|
| $\{1, 1, 1, 1, 10\}$ | $9$ | Clustered at low end |
| $\{1, 4, 5, 7, 10\}$ | $9$ | Evenly spread |
Both have range $9$, but they are distributed very differently. The range does not describe how spread out the middle values are.
Key Takeaway: Range is sensitive to outliers. A single extreme value can make the range misleadingly large.
Visual: Two Data Sets with the Same Range but Different Spread
Interactive visualization — available in the full lesson