Skewness and Data Distribution

Skewness and Kurtosis

• Not all data is normally distributed; understanding skewness is essential.
• Skewness describes the symmetry of a distribution.
• Kurtosis describes the peak of a distribution (advanced topic).

Skewed Distributions

• Skewed distributions can be positively or negatively skewed.
• Positive Skew:
  • Extreme scores fall at the positive tail of the distribution.
  • The mean is pulled towards the positive tail due to these extreme scores.
  • Example: A difficult test with mostly low grades.
• Negative Skew:
  • Extreme scores fall at the negative tail of the distribution.
  • The mean is pulled towards the negative tail.
  • Example: An easy test with mostly high grades (A's and B's).

Examples of Skewness

• Distributions can take various shapes and sizes.
• Positive skew: A large hump with extreme scores on the positive tail.
• Negative skew: Extreme scores on the negative tail.
• It is important to differentiate between positive and negative skews based on where the extreme scores lie.

Outliers and Their Impact on the Mean

• Outliers significantly affect the mean.
• Example: Including Bill Gates in a class's net worth calculation would drastically inflate the mean.

Advertisements and Skewness

• Advertisements may use extreme scores to manipulate the mean for marketing purposes.
• The median, representing the middle point, can be a more reliable measure than the mean when outliers are present.