Construct or read a percentage segmented bar chart

What should be done to find the endpoint after a segment?

Predict what changes when the same travel counts are displayed as percentages. Compare view 1 (stacked counts) with view 2 (100% stacked bars). Check both total heights and the Bus segments

Why do the whole bars become equal in view 2?

Percentage segmented bar charts

A percentage segmented bar divides one complete bar into category segments. Calculate the percentage width of each segment, add the widths in order to find endpoints, and check that the bar finishes at 100%

1. 1Find each percentage Divide each category frequency by the sample size and multiply by 100. \(\displaystyle p_i=\frac{f_i}{n}\times100\%\)
2. 2Keep the category order Place the segments in the stated order because the order is part of the display \(\displaystyle A\;\rightarrow\;B\;\rightarrow\;C\)
3. 3Accumulate the endpoints Add each segment percentage to the endpoint already reached \(\displaystyle C_i=C_{i-1}+p_i,\quad C_0=0\%\)
4. 4Check the complete bar The last cumulative endpoint must be 100% so every record is represented \(\displaystyle C_k=100\%\)

Category frequency

\(\displaystyle 8\)

Sample size

\(\displaystyle 40\)

A category has frequency 8 in a sample of 40. Find its percentage frequency

First segment

\(\displaystyle 30\%\)

Second segment

\(\displaystyle 20\%\)

The first segment is 30% and the next segment is 20%. Find the endpoint after the second segment

Using a segment length as an endpoint. One of these lines is right. Which one?

Produce two percentage segmented bars

In an invented travel survey, the morning session has 12 Bus and 8 Walk responses; the afternoon session has 20 Bus and 20 Walk responses. Each person gives one response. Draw one complete 100% segmented bar per session, with Bus followed by Walk from zero

1. 1Choose and use a function Use a 100% stacked bar or column function and explain why it suits comparing shares in different-sized groups. Record the counts, group totals, data orientation, category order and percentage-scale settings. Include labels and a legend
2. 2Verify and interpret Calculate every segment percentage and cumulative endpoint by hand to check the tool. Compare Bus using both counts and percentage points. State why equal total bar lengths do not establish equal numbers of respondents

Model response: Produce two percentage segmented bars

Other correct layouts, technology functions and explanations are possible

1. 1Percentages and endpoints Morning total: 20. Bus is 60% and Walk is 40%. Endpoints from zero are 60%, 100%. Afternoon total: 40. Bus and Walk are each 50%; endpoints are 50%, 100%. Use the same category order in both bars \(\displaystyle \frac{12}{20}\times100\%=60\%,\quad\frac{8}{20}\times100\%=40\%\)
2. 2Complete display and technology record Enter sessions as the two groups and Bus/Walk as the two series, then choose a 100% stacked chart. Check the tool has made one bar for Morning and one for Afternoon; switch rows and columns if necessary. Use a 0–100% scale, label Morning (n=20) and Afternoon (n=40), and include a Bus/Walk legend. The total lengths are equal because each represents its own complete group
3. 3Independent verification Check 60+40=100 and 50+50=100, and compare each boundary with its cumulative total. The morning Bus share is 60−50=10 percentage points higher. The afternoon has more Bus respondents, 20 compared with 12. A stacked count chart would show totals 20 and 40 instead of two complete percentage bars
4. 4Self-review checklist Check both totals, all four percentages, segment order and endpoints, equal whole-bar lengths, labels, sample sizes, legend, a reproducible tool record and a comparison that distinguishes counts from shares

This model uses a shared percentage scale. What do its equal total bar heights establish?