Statistics: Histograms and Frequency Tables

Histograms

• A pictorial method for representing frequency data; similar to a barchart.
• Data is measurable (e.g., lengths) not categorical (e.g., colors).
• Area of the bar in the histogram is proportional to the frequency.

Frequency Distribution Table

• A table containing grouped data, providing a clearer picture than individual data values.
• Used in the construction of histograms, barcharts, pie charts, dotplots, stem-and-leaf plots, and boxplots.

Constructing a Frequency Distribution Table

• Step 1: Find the range of the data.
• Step 2: Determine class intervals, initially all of the same width.
• Step 3: Construct a frequency distribution table.
• Step 4: For scarce data at extremes, combine classes.
• Step 5: If central frequencies are too high, split classes.
• Step 6: If class intervals are not equal, calculate frequency densities.

Frequency Densities

• Frequency density = frequency / class width

Drawing a Histogram

• Step 1: Close any open intervals with sensible limits.
• Step 2: Label both the horizontal and vertical axes, usually frequency or frequency density appears on the vertical axis.
• Step 3: The horizontal axis represents the values at the interval centers for discrete data, and at the interval boundaries for continuous data.
• Step 4: The areas of the bars are proportional to the frequency. For example, doubling the width of a bar would require halving its height to maintain the same frequency.
• Step 5: For discrete data the horizontal axis shows the values at the interval center, and for continuous data, the horizontal axis represents the interval boundaries.