CH 2: Exploring and Summarizing Data

Learning how to describe variables

What are the two kinds of quantitative variables?

Continuous and discrete

Continuous variables

Taking any value within an interval, no minimum distance between 2 observable values; limitless

Discrete variables

Minimum distance between measurements, taking values at a fixed minimum distance, keeping track at how many times something happens

What is frequency?

Number of occurrences of a categorical variable; represents the number of observations for each category of data

What are we interested in when looking at observations within a certain category?

Its proportion and percentage

Equation for proportion

Frequency (from a specific category) / Sample size (n)

Equation for percentage

proportion x 100%

What are the two primary graphs for a categorical variable

Bar graph and pie chart

Bar graphs contain

1. Categories on the horizontal axis (x-axis)

2. Frequencies (or proportions) on the vertical axis (y-axis)

3. Heights of the rectangles for each category is equal to the category’s frequency or proportion

Describe a pie chart

• Circle divided into sectors

• Sectors = a category of data

• 2 weaknesses

  • If a subject goes into more than 1 category, percent sum > 100%

  • Too many categories will make it hard to read

To know what proportion selected one repose or another response:

Add number of respondents for those categories together / total number of respondents

In order to show that 2 categorical variables are related to each other use a

Contingency table

Contingency tables

Analyzes how one variable may relate to another variable

Describe histograms

• Use bars to display frequencies of possible outcomes of a quantitative variable

• Horizontal axis (x-axis) = breaks the data into ranges of values the variable can take

• Vertical axis (y-axis) = How many observations are within each certain range of values

Actual observed values come from the horizontal axis (x-axis)

What does the shape of a histogram or dot plot describe?

The distribution of the data

Shape only describes ___

quantitative data

What is modality?

Mode

What is mode?

High-point or most-frequent observation of the dataset; number or response that occurs most frequently

Unimodal

Data with one high point or one mode

Bimodal

Data with two peaks or high points or two modes

Look at the heights of the bars drop and then rise again across multiple bars separating the two modes