While mean, median, and mode describe the centre of a data set, measures of spread describe how spread out the data is. The Digital SAT tests range, standard deviation (conceptually — you won't calculate it by hand), and the effect of outliers on statistics.
Core Concepts
Range
Simple but sensitive to outliers.
Standard Deviation
Measures how far data values typically are from the mean. On the SAT, you need to understand the concept, not calculate it.
- Small SD: data clustered close to the mean.
- Large SD: data spread far from the mean.
Effect of Outliers
An outlier is a value far from the rest of the data.
- Mean: strongly affected by outliers (pulled toward the outlier).
- Median: resistant to outliers (stays near the middle).
- Range: strongly affected (outlier increases the range).
- Standard deviation: increased by outliers.
When to Use Mean vs. Median
- Symmetric data (no outliers): mean and median are similar; either works.
- Skewed data or outliers: median is a better measure of centre.
Comparing Spreads
If asked which data set has greater variability, compare standard deviations or ranges. A data set like {48, 49, 50, 51, 52} has less spread than {10, 30, 50, 70, 90}.
Strategy Tips
Tip 1: You Won't Calculate SD by Hand
The SAT only asks you to compare or reason about SD — never compute it.
Tip 2: More Clustered = Smaller SD
Data tightly clustered around the mean has a small standard deviation.
Tip 3: Adding/Removing a Data Point
If you add a value close to the mean, SD barely changes. If you add a value far from the mean, SD increases.
Tip 4: Adding a Constant to All Values
Adding the same number to every value doesn't change the SD (it shifts all values equally).
Tip 5: Multiplying All Values by a Constant
Multiplying every value by multiplies the SD by .
Worked Example: Example 1
Data: {3, 7, 8, 8, 10, 12, 50}. Which measure of centre best represents the data?
Mean = . Median = 8. The outlier (50) pulls the mean up. Median is better.
Worked Example: Example 2
Which has the greater standard deviation: {20, 20, 20, 20} or {10, 15, 25, 30}?
First set: all values identical → SD = 0. Second set: values vary → SD > 0.
Worked Example: SAT-Style
Set A: {10, 12, 14, 16, 18}. Set B: {2, 8, 14, 20, 26}. Both have mean 14. Which has greater SD?
Set B has values farther from 14 → Set B has greater SD.
Worked Example: Example 4
If 5 is added to every value in a data set, what happens to the mean, median, range, and SD?
Mean: increases by 5. Median: increases by 5. Range: unchanged. SD: unchanged.
Practice Problems
Problem 1
Find the range of {4, 7, 12, 15, 23}.
Problem 2
Which data set has a larger SD: {5, 5, 5, 5} or {3, 5, 7, 9}?
Problem 3
A class has test scores: {55, 72, 74, 76, 78, 80, 95}. Is the mean or median a better measure of centre?
Problem 4
All values in a data set are doubled. What happens to the SD?
Problem 5
If an outlier is removed from a data set, what happens to the mean and SD?
Want to check your answers and get step-by-step solutions?
Common Mistakes
- Thinking mean is always the best measure. With outliers, median is better.
- Confusing range with standard deviation. Range is just max − min. SD considers every data point.
- Thinking adding a constant changes SD. Adding a constant shifts data without spreading it.
Key Takeaways
Range = max − min. Simple but sensitive to outliers.
SD measures typical distance from the mean. You won't compute it — just reason about it.
Outliers pull the mean and increase the range and SD.
Median resists outliers — use it for skewed data.
Adding a constant to all values: mean and median shift; SD stays the same.