Focuses on the importance of using statistics to inform decisions.
Emphasizes organizing and summarizing data effectively.
Organize discrete data in tables.
Construct histograms of discrete data.
Organize continuous data in tables.
Construct histograms of continuous data.
Draw dot plots.
Identify the shape of a distribution.
Identify the Type of Data
Discrete Data: Countable values (e.g., number of students: 20, 21, 22).
Continuous Data: Measured values that can take any number in a range (e.g., height: 5.6 ft, 5.75 ft).
How to Categorize Data
Few Discrete Values: Use actual observations as categories.
Example: Number of Pets vs. Frequency (0: 10, 1: 15, 2: 8, etc.).
When to use: If few values makes sense and is easy to interpret.
Many Discrete Values or Continuous Data: Group into intervals.
Example for Height Range and Score Range.
Use intervals when too many different values make listing impractical, allowing visible patterns.
Example from a Wendy's restaurant regarding customer data collection over 15-minute intervals.
Importance of creating frequency and relative frequency distributions.
A histogram consists of rectangles for each data class:
Height represents frequency or relative frequency.
Rectangles should touch each other.
Data must be categorized into groups/classes:
Lower class limits (smallest value) and upper limits (largest value).
Class width is the difference between lower class limits.
Example illustrating the age of mothers having children in a specific year.
Choose the smallest data observation or a convenient number slightly lower than it for the lower limit.
The number of classes should usually be between 5 and 20.
Class width calculated as: (largest data value - smallest data value) / number of classes, rounded to a convenient number.
Similar to discrete histograms but considers continuous data.
Example using fine values.
Dot plots represent each observation horizontally, with dots above each occurrence.
Types of Distributions:
Uniform: Frequencies evenly spread.
Bell-shaped: Highest frequency in the middle, tails taper off.
Skewed right: Longer tail on the right.
Skewed left: Longer tail on the left.
Note: Qualitative data does not match these characteristics.
Draw stem-and-leaf plots.
Construct frequency polygons.
Create cumulative frequency and relative frequency tables.
Construct frequency and relative frequency ogives.
Draw time-series graphs.
Left digits form the stem; rightmost digit is the leaf.
Example given showing poverty percentages by state.
Manipulating Vertical Scale: Misleading interpretations created by non-starting y-axis at zero.
Three-Dimensional Graphics: These can exaggerate categories visually.
Guidelines for better graphics: clear titles, avoid distortion, minimize whitespace, coherent designs.
I can't provide images directly, but I can describe some popular data displays that you might find useful:
Bar Charts: Useful for comparing categorical data. Each category is represented by a rectangular bar with length proportional to the value it represents.
Histograms: Display frequency distributions of numerical data, where data is divided into intervals (bins).
Pie Charts: Show proportionate data as slices of a pie, useful for illustrating percentage breakdowns.
Line Graphs: Great for showing trends over time, using points connected by lines to depict data changes.
Dot Plots: Represent individual data points on a simple axis, useful for small datasets.
Box Plots: Show the distribution characteristics such as median, quartiles, and outliers of a dataset.
Scatter Plots: Used to determine relationships between two numerical variables, displaying values for typically two variables for a set of data.
To see these displays, I recommend checking online resources or data visualization tools.