AP Statistics / Unit 1: Exploring One-Variable Data and Collecting Data
1.7 Summary Statistics for One Quantitative Variable
Notes
- Mean $\bar x$: sum ÷ count. Not resistant to outliers.
- Median: the middle value. Resistant.
- Standard deviation $s_x$: typical distance from the mean. IQR $=Q_3-Q_1$.
- Outlier rule: below $Q_1-1.5\,IQR$ or above $Q_3+1.5\,IQR$.
Practice
Data: 2, 4, 4, 5, 10. The median:
Middle value.
$Q_1=20$, $Q_3=30$. The upper outlier fence:
$30+1.5(10)$.
In a strongly right-skewed distribution, usually:
The tail pulls the mean.
Ready for more? Take the Unit 1 test.