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STA291. Statistical Methods Lecture 9. About those boxplots …. Often used to compare samples (& make inferences about populations) Example: Barry Bonds’ home runs. Boxplots or other graphs used for comparison/outlier checking:. The good: Quick Simple

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STA291

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## STA291

Statistical Methods

Lecture 9

Often used to compare samples (& make inferences about populations)

Example: Barry Bonds’ home runs

### Boxplots or other graphs used for comparison/outlier checking:

• The good:

• Quick

• Simple

• Don’t depend on distribution of sample

• The not-so-good:

• Non-numeric

• Depend on samples being compared having same units

### 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.

### 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.

### Empirical Rule Example

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 ___________%?

### Looking back

• Side-by-side boxplots

• z-scores

• Empirical, or 68-95-99.7 Rule