Constructing Histograms (and the Zero-Frequency Trap)

A histogram is a special type of bar graph built directly from a grouped frequency table. * The horizontal axis represents the continuous intervals. * The vertical axis represents the frequency. * The Rule of Touching Bars: Because the intervals are continuous numbers, the bars MUST touch each other with no spaces between them. * The Zero-Frequency Trap: If an interval has no data (frequency of 0), the bar height is 0. You must leave that space c

Example: Standard Histogram: Using the quiz scores from the previous section, you would draw three touching bars. The bar for 70-79 goes up to 4, the bar for 80-89 goes up to 5, and the bar for 90-99 goes up to 3.

Zero-Frequency Gap: A dataset of ages uses intervals of 10. The 10-19 age group has 5 people, the 20-29 group has 0 people, and the 30-39 group has 3 people. On the histogram, you must draw the 10-19 bar, leave a blank space exactly one bar wide for the 20-29

Think of a histogram as a city skyline where each building represents a group of data. The buildings have no gaps between them because the numbers flow continuously from one interval right into the next.

Constructing Histograms (and the Zero-Frequency Trap) is a Grade 6 math topic covered in Reveal Math, Course 1 in Module 10: Statistical Measures and Displays. Students at this level study the concept as part of their grade-level standards and are expected to explain, analyze, and apply what they have learned.

The buildings have no gaps between them because the numbers flow continuously from one interval right into the next. The taller the building, the more data points are packed inside that specific range. The only time you will ever see a gap between buildings is if an interval is completely empty (a frequency of zero)..