Lecture_6 Flashcards
(13 cards)
Arithmetic Mean
Definition: The arithmetic average of all data points.
Data Sensitivity: Sensitive to all data points, especially outliers and extreme values.
Best for: Symmetric distributions where data is
evenly spread.
Use in Calculations: Essential for advanced statistical models (e.g., regression, variance, standard deviation).
Median
Definition: The middle value when data is sorted, or the average of the two middle values.
Data Sensitivity: Insensitive to outliers; only depends on the position of data in the sorted set
Best for: Skewed distributions or datasets with
outliers.
Use in Calculations: Rarely used in further calculations.
Mode
Quartile
Range
π ππππ = πππππππ π‘β ππ ππππππ π‘
Interquartile range
πΌππ‘ππππ’πππ‘πππ π ππππ = π3β π1
Variance
Variance = standard deviation (sigma)^2
Variance = standard deviation (s)^2
Standard deviation
sigma for population
s for sample
Distribution shape symmetrical
Mean =
Median =
Mode
Distribution shape right-skewed
Right Skewed:
* Mode < Median < Mean
* Mean > Median: some unusually high values
Shape: Right (Positively)-Skewed Distribution
HΓΌgel links
Distribution shape left-skewed
Left Skewed:
* Mean < Median < Mode
* Mean < Median: some unusually low values
Shape: Left (Negatively)-Skewed Distribution
HΓΌgel rechts
Empirical rule
The Empirical Rule (68/95 Rule)
- About 68% of all observations are contained within the distance of one standard deviation around the mean
- About 95% of all observations are contained within the distance of two standard deviations around the mean
Six Sigma and the Empirical Rule
Six Sigma & Empirical Rule
* Methodology for near-perfect quality via reduced
process variation
* Focus on standard deviations:
* 1 Sigma β 68% defect-free,
* 6 Sigma β 99.99966% defect-free
β’ 3.4 defections per million opportunities
