Histograms and dot diagrams

A histogram groups numerical measurements

These equal-width classes have adjacent bars; the horizontal positions and widths represent numerical intervals. Unlike a category bar chart, gaps between these classes would suggest missing ranges. The boundary rule places a time of exactly 20 minutes in the second class, once only.

Construct a truthful display

Draw the travel-time histogram from its table. Label both axes and use equal horizontal widths for the equal 10-minute classes. A graph preserves the grouped counts, but cannot recover each pupil’s exact travel time inside a class.

A dot diagram retains individual values

For 0,1,1,2,4,4,4, place one dot per observation above its value on a common number line. Stack repeated values at the same horizontal position. There are seven dots, with three at 4 and none at 3. A gap can be meaningful; do not spread repeated values sideways as if they were different measurements.

Check your understanding 1 Count observations, not occupied positions

A dot diagram has two dots at 1, one at 2 and four at 5. How many observations are there, and what is the most common value?

Your answer or drawing on paper

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There are 7 observations and the modal value is 5. Three occupied positions do not mean three observations; the stacks preserve repeated values.