1. Types of variables Discrete VS Continuous Discrete Continuous
Analogous to number of things
Continuous
Analogous to amounts
“the number of” VS “the amount of”
The number of cigarettes smoked
This amount of nicotine consumed

2. Exercises
Specify whether each of the following measurements are discrete or continuous
The number of stairs in a building
The height of a tree measured as precisely as possible
The number of pages in a book
The weight of a book

3. Displaying data using graphs
Categorical Data
1. Pie Charts
Show percentages
Depict relative size of groups

4. Displaying data using graphs
2. Bar Graphs
Show percentages or frequencies in various categories
Can depict two variables simultaneously
Can represent proportions that do not sum up to 100%

5. Displaying data using graphs
The same data can be displayed in more than one type of graph:

6. Displaying Data Using Graphs
Quantitative Variables
1. Line graphs/time plots
Display a series of observations in sequence
Time, depth, height
Sequence must be continuous
Shows change and rate of change
Detect trend

8. Displaying Data Using Graphs
Quantitative Variables
2. Histograms
Describe the shape of a variable’s distribution
Provide idea of
Center
Spread
Outliers
Shape

9. Displaying Data Using Graphs
Center
Midpoint
Most frequently occurring values
Spread
Variation about the center
Highs, lows, range
Outliers
Values that lie outside of the data range

10. Displaying Data Using Graphs
Shape
Symmetric Distribution
Left and right sides of a histogram on either side of the center frequency are mirror-images if each other

11. Displaying Data Using Graphs
Shape
Skewed Distribution
Not symmetrical
Skewed to the left (-)
Lower values are more spread out than higher values
Skewed to the right (+)
Higher values are more spread out than lower values

12. Displaying Data Using Graphs
Distribution Shapes and Characteristics
Unimodal Distribution
When histogram only shows one prominent peak
Bimodal Distribution
When there are two prominent peaks observed

13. Displaying Data Using Graphs
3. Stemplots (Stem and leaf diagrams)
Shape of values
Range
Variation
Outliers

14. Describing Distributions with Numbers
Distribution Summary – a set of descriptive statistics that summarize its distribution.
Central tendency
Spread