Measurement Variables Describing Distributions © 2014 Project Lead The Way, Inc. Computer Science and Software Engineering

A nearly perfect analogy continuous : discrete analog : digital float : int Measurements of continuous variables are made discrete by "binning" them. How old are you? Time is continuous, but you answer in discrete, binned values. Continuous vs. Discrete

Categorical (e.g., zip codes) categories with no meaningful order Ordinal (e.g., rank in a race) ordered, but increasing by 1 has no consistent meaning Interval (e.g., grade level) Ordered, with consistent steps up, but no meaning for "doubling" or "tripling" Ratio (e.g., height) Ordered, with "2 times" being "double" Levels of a Measurement Variable

Sample vs. Population Population = infinite pool of measurements, or all measurements possible Sample = subset of population

Sample vs. Population

Infer population distribution from sample histogram Sample histogram matches parent distribution better with large sample visualized with small intervals

Half of the area under the distribution is to the left of the median Median

Mean, Median, Mode

y-axis shows values of the data Splits data into quartiles Box Plot height

Each box contains 25% of the data The IQR (Interquartile Range) Contains 50% of the Data

Whiskers extend to max and min… usually Box Plot

Whiskers and Outliers Show max/min

The Range Contains 100% of the Data

A family of distributions with very similar shape One normal distribution for each μ and σ Normal Distributions μ σ μ ("mu") = population mean σ ("sigma") = population standard deviation

One normal distribution for any pair μ, σ Example: μ = 6 and σ = 2.2 A Normal Distribution μ σ μ ("mu") = population mean σ ("sigma") = population standard deviation

μ = 0 and σ = 1 The Standard Normal Distribution μ σ

The Empirical Rule: 67% - 95% % 67% area95% area99.7% area values within μ ± σ values within μ ± 2σ values within μ ± 3σ

Shape, Center, Spread These distributions are both positively- skewed because they are right-tailed

Shape, Center, Spread