Lesson on Histograms

Introduction

• Histogram: A bar graph that represents a frequency distribution.
  • Width: Represents the interval.
  • Height: Represents the corresponding frequency.
  • No spaces between bars.

Key Concepts

• Intervals/Bins: Categories represented on the horizontal axis.
• Vertical Axis: Indicates frequency.
• Mode of Wait Times: Identified by the highest bar.

Constructing a Histogram

1. Data Example: Average gas mileage of 20 cars.
2. Frequency Table:
   • Establish intervals with equal width.
   • Total of 7 intervals (bins).
3. Tally Data: Assign data points to intervals.
4. Determine Frequencies: Number of data points in each interval.
   • Frequencies: 2, 4, 5, 4, 2, 2, 1.

Creating the Histogram

• Horizontal Axis:
  • Divide into 7 equal intervals (bins).
• Vertical Axis:
  • Max frequency of 6.
  • Construct bars based on frequencies:
    • Interval 10-14: Height 2
    • Interval 15-19: Height 4
    • Interval 20-24: Height 5
    • Interval 25-29: Height 4
    • Further intervals: Heights 2, 2, 1

Additional Points

• Mode of Data: Interval 20-24 for average gas mileage.
• Histogram Software: Example created using Excel.

Special Considerations

• Continuous Data:
  • Last data value of a bin often first in the next bin.
  • Example: Heights of Black Cherry Trees.
  • Interval notation: Closed on starting value, open on ending value.

Example of Intervals:

• Interval 60-65: Closed on 60 (includes 60), open on 65 (excludes 65).
• Next interval 65-70: Closed on 65, open on 70.

Conclusion

• Importance of understanding interval notation and labeling in histograms.
• Ensure clarity on data point placement within intervals.