Overview
This lecture introduces histograms as a preferred method for displaying large sets of numerical data, explains their construction, and covers concepts such as bin width and relative frequency.
Introduction to Histograms
- Histograms are used to display large datasets of numerical variables.
- Unlike dot plots, histograms use bars (rectangles) and group data into bins for efficiency.
Components of a Histogram
- The x-axis (horizontal) represents the variable of interest (e.g., number of home runs).
- The y-axis (vertical) represents the frequency (number of occurrences in each bin).
- Bins are equally sized intervals on the x-axis where data points are grouped.
Creating and Interpreting Histograms
- Data is sorted into bins by value; the height of each bar shows the frequency for that range.
- To avoid overlap, the left value of a bin is included, but the right is not (interval notation).
- Example: For home runs, the first bin might be 80 to 129, including 80 but excluding 130.
Bin Width and its Effects
- Bin width is the range each bin covers (e.g., 50 or 10).
- Changing bin width alters the histogram's shape and interpretation.
- The choice of bin width is important for accurately displaying data trends.
Relative Frequency Histograms
- Relative frequency is the fraction of observations in a bin (frequency divided by total number, n).
- Relative frequency histograms have decimals or percentages on the y-axis instead of counts.
- The x-axis and bin width remain unchanged when switching between frequency and relative frequency histograms.
Key Terms & Definitions
- Histogram — A bar graph for numerical data, grouping data into intervals (bins) on a number line.
- Bin — An interval grouping data points on the x-axis.
- Bin Width — The size of each bin; determines how data is grouped.
- Frequency — The count of data points within a bin.
- Relative Frequency — The proportion of data points in a bin, often shown as a decimal or percentage.
- n — The total number of observations in the dataset.
Action Items / Next Steps
- Practice creating histograms with sample data, adjusting bin widths.
- Calculate frequency and relative frequency for given datasets.
- Review reading on Chapter 1 as foundation for these concepts.