lOMoARcPSD| 62788957
Applied Probability and
Statistics
Class C955 Applied Probability and Statistics
Descriptive Statistics for a Single Variable
🎯 Learning Objectives
By the end of this module, you should be able to:
Apply the standard deviation (empirical) rule
Choose appropriate statistical measures
Calculate and interpret mean, median, mode, quartiles, range, IQR, and standard
deviation
Describe data distributions in context
Use and interpret various graphs for categorical and quantitative data
🎯 Types of Data
Quantitative Numeric values (e.g., salaries, height)
Categorical Group labels (e.g., job titles, zip codes)
🎯 Graphical Displays For
Categorical Data:
Bar Charts Compare category frequencies Pie
Charts Show proportions of a whole For
Quantitative Data:
Applied Probability and Statistics
, lOMoARcPSD| 62788957
Dot Plots Display individual data points
Stem-and-Leaf Plots Show distribution by place value, shows both the shape of the
data and individual data points
Histograms Show frequency over intervals, used for continuous data
Box Plots Summarize spread using quartiles, good for including outliers
🎯 Measures of Center
Mean Average (use when data is symmetric)
Median Middle value (use when data is skewed) (middle value of graph) Mode Most
frequent value (can have multiple) (peak of the graph)
🎯 Measures of Spread
Range Max Min
Interquartile Range IQR Q3 Q1 (shows middle 50%
Standard Deviation Average distance from the mean (for symmetric data)
🎯 Describing Distributions
Symmetric Bell-shaped or uniform
Skewed Left Negatively Skewed) Tail on left, Mean Median Mode
Skewed Right Positively Skewed) Tail on right, Mode Median Mean Bimodal or
Multimodal Multiple peaks
🎯 Empirical (Standard Deviation) Rule
For normal distributions:
Applied Probability and Statistics 2
, lOMoARcPSD| 62788957
68% of data within 1 SD of the mean 95%
within 2 SDs
Applied Probability and Statistics
Applied Probability and
Statistics
Class C955 Applied Probability and Statistics
Descriptive Statistics for a Single Variable
🎯 Learning Objectives
By the end of this module, you should be able to:
Apply the standard deviation (empirical) rule
Choose appropriate statistical measures
Calculate and interpret mean, median, mode, quartiles, range, IQR, and standard
deviation
Describe data distributions in context
Use and interpret various graphs for categorical and quantitative data
🎯 Types of Data
Quantitative Numeric values (e.g., salaries, height)
Categorical Group labels (e.g., job titles, zip codes)
🎯 Graphical Displays For
Categorical Data:
Bar Charts Compare category frequencies Pie
Charts Show proportions of a whole For
Quantitative Data:
Applied Probability and Statistics
, lOMoARcPSD| 62788957
Dot Plots Display individual data points
Stem-and-Leaf Plots Show distribution by place value, shows both the shape of the
data and individual data points
Histograms Show frequency over intervals, used for continuous data
Box Plots Summarize spread using quartiles, good for including outliers
🎯 Measures of Center
Mean Average (use when data is symmetric)
Median Middle value (use when data is skewed) (middle value of graph) Mode Most
frequent value (can have multiple) (peak of the graph)
🎯 Measures of Spread
Range Max Min
Interquartile Range IQR Q3 Q1 (shows middle 50%
Standard Deviation Average distance from the mean (for symmetric data)
🎯 Describing Distributions
Symmetric Bell-shaped or uniform
Skewed Left Negatively Skewed) Tail on left, Mean Median Mode
Skewed Right Positively Skewed) Tail on right, Mode Median Mean Bimodal or
Multimodal Multiple peaks
🎯 Empirical (Standard Deviation) Rule
For normal distributions:
Applied Probability and Statistics 2
, lOMoARcPSD| 62788957
68% of data within 1 SD of the mean 95%
within 2 SDs
Applied Probability and Statistics
