What this lesson teaches
I can read and choose the right maps, graphs, photographs and other visual resources.
Syllabus 8834, Fieldwork, Additional Notes on Data. Students are required to be familiar with the following types of data: Maps: contour maps, choropleth maps, isoline maps, dot maps, flow-line maps, proportional symbols maps and cartograms; Graphs: pie charts, bars, histograms, scatter graphs, radar charts, triangular graphs and line graphs; Photographs: landscape photographs, aerial photographs and satellite images; Others: tables, schematic diagrams, illustrations and cartoons.
Make a guess
A histogram has unequal class widths. One bar is the tallest. Does it hold the most observations?
- No, because the shortest bar holds the most.
- Yes. The tallest bar has the most.
- No, not necessarily. Area, not height, shows frequency.
- Yes, because height shows frequency directly.
Show the answer
No, not necessarily. Area, not height, shows frequency.
With unequal widths, height is frequency divided by width. A lower but wider bar can hold more observations.
In a histogram, bar area shows frequency, so with unequal intervals the height must be frequency divided by class width.
A histogram groups a continuous variable, like walking time, into intervals. The bars touch because the intervals join up. Define the boundaries clearly, such as "5 to under 10 minutes", so no value is counted twice.
Frequency density = frequency / class width. Eight people in a 5-minute interval gives a density of 1.6 people per minute. Twelve people in a 10-minute interval gives 1.2. That bar is lower but wider, so it holds more people.
To draw one, put the variable on the horizontal axis and density on the vertical axis. Make each bar the true width of its interval. To find frequency, multiply height by width.
Grouping loses exact values. Different interval choices can change how the pattern looks, so keep the original data.
- Frequency density
- Frequency divided by class width.
- Bar area
- Shows frequency.
- Unequal intervals
- Compare areas, not heights.
Step by step
Find the widths
Upper minus lower boundary.
Find the heights
Frequency divided by width.
Check the areas
Height times width gives each frequency.
Worked example: Reading one bar
The 20-to-under-40-minute bar has a height of 0.4 people per minute and a width of 20 minutes. So it holds 0.4 x 20 = 8 people, the same as the much narrower 5-to-under-10 bar.
Watch out for this
The tallest bar always has the most people.
That is only true if all intervals are equal. Otherwise, compare areas.
Check your understanding
A 10-minute interval holds 15 journeys. What density should be plotted?
- 1.5 journeys per minute.
- 0.15 journeys per minute.
- 150 journeys per minute.
Show the answer
1.5 journeys per minute.
Yes. 15 / 10 = 1.5.