Bus' Stats' - Quantitative Measurement Concepts

Ordinal

Categorical Data w/ no inherent oder or ranking

• Colors

• Gender

• Country

• Blood Types

Nominal

Categorical Date WITH a natural, meaningful order or ranking

• Education Level

• Movie Ratings in Stars

• Low/Middle/High

μ

mean_population

x̄

mean_sample

σ²

Variance_population

s²

Variance_sample

σ

Standard Deviation _population

s

Standard Deviation _sample

MAD (Def.)

Mean Absolute Deviation: The average of the sum of all absolute differences between each data point and the overall dataset’s mean

MAD_population

MAD_sample

Variance (Def.)

A squared unit of measurement that is designed to be sensitive to outliers in datasets and used to measure volatility (usually risk) of a dataset through averaging the overall squared differences between each of the individual data points and the mean of the dataset. The less the value, the less the volatility; vice versa. The variance value (volatility) of one dataset is useful for comparing dispersion within that dataset or with other datasets ONLY when the other datasets share similar means and units. Variance values are the stepping stones to calculating the Standard Deviation of a dataset, which represents the ABSOLUTE volatility of a dataset, and is more tangible and intuitive for conceptualizing the volatility of real-life datasets.

Variance_population

Variance_sample

[ σ ] Standard Deviation _population

[ s ] Standard Deviation _sample

Coefficient of Variation (Def.)

A dimensionless/unitless measurement used to assess volatility relative to a dataset (risk per unit of return), which is utilized to compare volatilities between different datasets regardless of differences in means and units within those datasets.

Coefficient of Variation _population

Coefficient of Variation _sample

Interval Data

Numerical Data with Equal Intervals between values but NO ABSOLUTE ZERO POINT

• Temperature

• Calendar dates

Cannot multiply meaningfully

Ratio Data

Numerical Date w/ Equal Intervals AND a ABSOLUTE ZERO POINT (complete absence)

• Height / Weight

• Age

• Income / Expenses

• Distance / Time

• Number of Items

Random Variables

A variable who’s value is determined by the outcome of a random phenomenon

Discrete RV

Finite set of distinct values / integers

• Students in a class

• Dice outcomes

• 1, 2, 3, 4, 5, …

Continuous RV

Any value within an interval or range of real numbers

• Height

• Temperature

• Weight