Statistics Class: Lesson 3 Notes

Introduction

• Focus: Visualizing statistics through graphs.
• Topics: Frequency Distribution and Histograms.

Frequency Distribution

• Definition: A list, table, or graph showing the frequency of outcomes in a sample.
• Components:
  • Classes: Bins or intervals of data (e.g., income ranges).
  • Frequency: Count of data entries in each class.
  • Class Limits: Lower and upper boundaries of a class.
  • Class Width: Difference between consecutive lower class limits.

Example

• Class Example: Income ranges with frequencies.
  • 5 classes: e.g., $1-$20,000 frequency 5.
  • Class width: Consistent across classes.

Calculations

• Class Width: Calculate using consecutive lower limits.
• Frequency: Number of entries within each class range.
• Relative Frequency: Frequency of class divided by total, expressed as decimal or percent.
• Midpoint: Average of lower and upper limits.
• Cumulative Frequency: Total frequency up to and including the class.

Constructing a Frequency Distribution

• Steps:
  1. Decide number of classes (5-20).
  2. Calculate Class Width: (Max value - Min value) / Number of classes.
  3. Round up to nearest integer.
  4. Determine class limits.
  5. Tally frequencies.

Example

• Data: Daily high temperatures in May.
• Steps: Determine classes, calculate class width, and construct frequency distribution table.

Histograms

• Definition: Bar graph representing frequency distribution.
• Construction:
  • X-Axis: Class boundaries.
  • Y-Axis: Frequency.
  • Bars touch each other.

Shapes of Histograms

• Normal/Bell-Shaped: Low-high-low frequency, symmetric.
• Skewed Right: High frequency decreasing to the right.
• Skewed Left: High frequency decreasing to the left.
• Uniform: Even frequency across classes.
• Bimodal: Two peaks in frequency.
• Multimodal: Multiple peaks.

Importance of Shapes

• Shapes give insights into data distribution
• Normal distribution allows for advanced statistical analysis.

Conclusion

• Understanding frequency distributions and histograms is foundational.
• Next steps will explore additional statistical visualization methods.