2: Describing Data, Part 1

2: Describing Data, Part 1


Upon successful completion of this lesson, you will be able to:

  • Compute and interpret a basic proportion/risk/probability and odds
  • Select and interpret the appropriate visual representations for one categorical variable, two categorical variables, and one quantitative variable 
  • Use Minitab to construct frequency tables, pie charts, bar charts, two-way tables, clustered bar charts, histograms, and dotplots
  • Compute and interpret complements, intersections, unions, and conditional probabilities given a two-way table
  • Identify outliers on a histogram or dotplot
  • Interpret the shape of a distribution
  • Compute and interpret the mean, median, mode, and standard deviation
  • Compute and interpret percentiles and z scores
  • Apply the Empirical Rule
  • Interpret a five number summary

This lesson corresponds to Sections 2.1-2.3, and P.1 in the Lock5 textbook.

Recall from Lesson 1 that variables can be classified as categorical or quantitative:

Names or labels (i.e., categories) with no logical order or with a logical order but inconsistent differences between groups, also known as qualitative.
Numerical values with magnitudes that can be placed in a meaningful order with consistent intervals, also known as numerical.

The graphs, descriptive statistics, and inferential statistics that are appropriate depending on the nature of the variable(s) in a given scenario. Before beginning this lesson, you should be able to classify variables as categorical or quantitative. If you are having difficulties with this, go back to review Lesson 1 or speak with your instructor.

2.1 - Categorical Variables

2.1 - Categorical Variables

Categorical variables are discussed in Sections 2.1 and P.1 of the Lock5 textbook.

Variables can be classified as categorical or quantitative. In this section of the lesson, we will be focusing on categorical variables. Categorical variables are those that provide groupings that may have no logical order, or a logical order with inconsistent difference between groups (e.g., the difference between 1 and 2 is not equivalent to the difference between 3 and 4).

This course includes many examples and practice problems for you. Many of these will apply the concepts that we learn to experiments involving rolling a die or randomly selecting a card from a standard 52-card deck. If you are unfamiliar with either of these, take a moment here to review.


A standard die has 6 sides: 1, 2, 3, 4, 5, 6

52-Card Deck

A standard 52-card deck of playing cards has 13 Hearts, 13 Diamonds, 13 Spades, and 13 Clubs. Hearts (♥) and Diamonds (♦) are red suits. Spades (♠) and Clubs (♣) are black suits. For each suit, there is a 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. Jacks, Queens, and Kings are "face cards."