M

Chapter 1: The Standard Deviation

Range Rule of Thumb: Identifying Extreme Values

  • The range rule of thumb can be used to identify significantly high or significantly low data values.

  • A value is considered significantly high if it is more than two standard deviations above the mean.

  • A value is considered significantly low if it is more than two standard deviations below the mean.

  • This concept is represented by the formula: \text{Extreme Values} = \text{Mean} \pm 2 \cdot \text{Standard Deviation}

  • For example, if a question asks to determine significantly high or significantly low values using the range rule of thumb, you would add or subtract two standard deviations from the mean respectively.

Range Rule of Thumb: Approximating Standard Deviation

  • Distinct from identifying extreme values, the range rule of thumb can also be used to approximate the standard deviation of a dataset.

  • The approximation of the standard deviation is calculated by dividing the range (maximum value minus minimum value) by four.

  • The formula for approximating standard deviation using this rule is: \text{Approximate Standard Deviation} = \frac{\text{Range}}{4}

  • It is crucial to distinguish between these two applications of the range rule of thumb, as they serve different purposes.

Assessment Information

  • The instructor notes that questions specifically asking to use the range rule of thumb for identifying extreme values or approximating standard deviation (as described above) are not expected to be on the current main assessment or practice materials.

  • There will be sections within quizzes or separate assessments that may cover material not explicitly taught in class.

  • However, these specific quizzes or assessments will not contribute to or negatively impact the grade on the main test. They are standalone and separate grading components, intended perhaps for supplemental practice or to cover broader topic areas.