Overview
This lecture explains histograms, demonstrates how to construct them, and clarifies how intervals (bins) are organized and labeled.
Understanding Histograms
- A histogram is a bar graph representing a frequency distribution of data.
- The width of each bar shows the data interval (bin), and the height shows the frequency (count) in that interval.
- Histogram bars have no spaces between them, unlike bar charts.
- All bins (intervals) typically have equal width.
- The vertical axis always shows frequency.
Building a Histogram
- To construct a histogram, first organize data into a frequency table with set intervals (bins).
- Tally each data point into its corresponding interval/bin.
- Write down the frequency (count) for each bin.
- On the graph, the horizontal axis shows the bins, and the vertical axis shows their frequencies.
- Draw bars for each bin with heights equal to their frequencies.
Example: Gas Mileage Data
- Data from 20 cars was grouped into 7 bins with the following frequencies: 2, 4, 5, 4, 2, 2, 1.
- The mode (most frequent interval) was 20–24 miles per gallon.
Bin Boundaries and Inclusion
- When bins are next to each other with no gaps, the right endpoint of an interval is not included.
- For example: [60, 65) means 60 is included, but 65 is not; 65 is included in the next interval [65, 70).
- Always check how bin boundaries are defined when reading histograms.
Key Terms & Definitions
- Histogram — A bar graph for showing frequency distributions with no gaps between bars.
- Frequency — The count of data points within a specific interval/bin.
- Bin (Interval) — A range of data values grouped together on the horizontal axis.
- Mode — The interval/bin with the highest frequency.
- Interval Notation [a, b) — Includes a but excludes b; used to define bin boundaries.
Action Items / Next Steps
- Practice constructing histograms from raw data and interpret bin boundaries correctly.
- Review creating frequency tables as groundwork for making histograms.