In the example given, what does the standard deviation describe?

• A. The average number of acts of violence
• B. The variability of the data around the average
• C. The maximum observed value
• D. The overall trend over time

Answer: (B)

Standard deviation measures how spread out the data are around the average. It captures the typical distance of each value from the mean, so a small standard deviation means values cluster near the average, while a large one means the data are spread over a wider range. It doesn’t tell you the average value itself, the maximum observed value, or how something changes over time. For example, two data sets can share the same mean, but the one with a larger standard deviation has more variability around that average.