Overview
This lecture explains how to create histograms to visually represent frequency distributions and discusses key characteristics like class boundaries, equal bar widths, and skewness.
Drawing a Histogram
- A histogram is a bar graph displaying the distribution of data using adjacent bars of equal width.
- The horizontal axis represents data classes, typically marked with class boundaries.
- The vertical axis shows frequencies for each class, spaced evenly and marked to fit the highest frequency.
- Bars for each class rise to the frequency's height and are placed directly next to each other with no gaps.
- Each bar's width equals the class width, and all bars should be spaced evenly.
- Empty classes (frequency of zero) are shown as empty bars or gaps but the space must be preserved.
- Always include every possible class (even if frequency is zero) to keep even spacing.
Marking the Axes
- Preferred method: mark the horizontal axis with class boundaries (e.g., -0.5, 1.5, 3.5) for clarity and bar adjacency.
- Class midpoints can also be used as horizontal labels, but boundaries are more common.
- Do not use class limits that create ambiguous spaces or gaps between bars.
Histogram Features & Interpretation
- Bars must touch each other to be a true histogram.
- Histograms can reveal the distribution's shape: normal (bell-shaped) or skewed (asymmetrical).
- A skewed histogram has higher bars to one side, pulling the shape left or right.
- If the highest frequency is not in the middle, the distribution is not normal.
Key Terms & Definitions
- Histogram — A bar graph showing the frequency of occurrences for data classes, with bars touching.
- Class Boundaries — The exact edges between classes, used to label the horizontal axis.
- Class Width — The difference between class boundaries; all bars must have this equal width.
- Frequency — The number of data points in each class.
- Skewed Distribution — A histogram where one side has a longer tail; not symmetric or “normal.”
Action Items / Next Steps
- Practice drawing histograms using class boundaries and equal bar widths for provided data sets.
- Read textbook section on recognizing normal and skewed distributions in histograms.