Lecture Notes: Standard Deviation and Outliers

Importance of Standard Deviation

• Essential concept for the course.
• Frequent calculations required.

Definition of Outliers

• Outlier: A value outside the usual range of data values.
• Important for identifying errors or interesting data points.

Example

• Small cup of coffee price list: $2.39, $2.99, $3.09, $259 (no decimal).
• $259 likely an error or an interesting data point (luxury coffee).
• Importance of reviewing suspicious data points.

Identifying Outliers

• Not always obvious (e.g., the $259 coffee price is clear, others may be less so).
• No universal rule; methods vary among statisticians.

Class Definition of Outliers

• Rule: Data value more than two standard deviations away from the mean is considered an outlier.

Understanding Standard Deviation

• Mean: Central value of data.
• Standard Deviation: Average deviation from the mean.
• One Standard Deviation:
  • Above mean: ( \mu + \sigma )
  • Below mean: ( \mu - \sigma )

Two Standard Deviations

• Data beyond two standard deviations is rare.
• Two Standard Deviations Range:
  • Above mean: ( \mu + 2\sigma )
  • Below mean: ( \mu - 2\sigma )

Outliers

• Almost all data lies within two standard deviations of the mean.
• Values beyond this range are considered outliers.
• Finding Outliers:
  • Calculate mean and standard deviation.
  • Determine boundaries (two standard deviations above and below mean).
  • Values outside these boundaries are outliers.

Conclusion

• Identifying outliers helps in recognizing errors or understanding significant data points.
• Practical application in next examples.