1. STA291 Statistical Methods Lecture 9

2. About those boxplots … Often used to compare samples (& make inferences about populations) Example: Barry Bonds’ home runs First 11 Years Last 11 Years Minimum165 Q1Q1 2428 Median3340 Q3Q3 3746 Maximum4673

3. Boxplots or other graphs used for comparison/outlier checking: o The good: o Quick o Simple o Don’t depend on distribution of sample o The not-so-good: o Non-numeric o Depend on samples being compared having same units

4. An alternative: z-scores Often used to standardize individual values, either within samples/populations or between them, the z-score, or standardized score: is the number of standard deviations an observation is away from its mean.

5. Assumptions? Since both the population or sample versions of the z-score use the mean and standard deviation, we have the same concern when calculating it that we did when using the mean to describe the center of a distribution or the standard deviation to describe its variability. While it can be and sometimes is used in describing/comparing observations in the absence of knowledge about the distribution, more properly done so having determined that we have a “roughly symmetric and mound-shaped” distribution.

6. Outliers (& lots of useful stuff): Empirical, or 68-95-99.7 Rule 6

7. Empirical Rule Example 7 Distribution of SAT score is scaled to be approximately bell-shaped with mean 500 and standard deviation 100 About 68% of the scores are between __ ? About 95% are between ____ ? If you have a score above 700, you are in the top ___________%?

8. Looking back o Side-by-side boxplots o z-scores o Empirical, or 68-95-99.7 Rule