Finding the Center
Descriptive statistics summarize data without drawing broader inferential conclusions. Measures of central tendency describe a data set's typical value.
| Measure | Definition | Best used when... |
|---|---|---|
| Mean | Sum divided by count | Data is symmetric |
| Median | Middle value when ordered | Data is skewed or has outliers |
| Mode | Most frequent value | Data is categorical |
Common pitfall: Always defaulting to the mean without checking for outliers. One extreme value can drag the mean far from what is typical; the median is much more robust.
Measuring Spread
Measures of variability describe how spread out a data set is around its center. The range is the highest value minus lowest, but it is sensitive to just two extreme points.
Variance measures the average squared distance of each point from the mean. The standard deviation (SD) is the square root of variance, expressing spread in original units:
| Measure | What it captures |
|---|---|
| Range | Total spread (high minus low) |
| Variance | Average squared distance |
| Standard deviation | Spread in original units |
A small SD means data clusters tightly; a large SD means wide spread.