LogicalDUAL-USE

Cumulative Graph Trick

What it is

Plotting a running total instead of the per-period figure, so that the line can only rise and a slowdown, a decline or a collapse in the underlying rate appears as a still-climbing curve.

How it works

A cumulative series adds each period's value to everything before it, so as long as the per-period number is not negative the line goes up. Worked: quarterly sales of 100, 90, 80 and 70 give cumulative totals of 100, 190, 270 and 340 — a rising line drawn over a business whose sales have fallen by 30 percent. The decline is present in the chart only as a slight flattening of the slope, which the eye does not read, especially when the line is smoothed, the scale is tall and the annotation says “growth”. Audiences read up-and-to-the-right as success because that is what it means on a per-period chart, and the presenter borrows that reading. Cumulative charts have honest uses: total installed base, money raised toward a goal, cumulative emissions, where the total is the quantity that matters. They mislead when the audience wants to know the rate and is shown the sum, and the presenter chose the sum because the rate has turned. The tell is a cumulative chart without the per-period series beside it, offered in a context — quarterly results, a fundraising pitch, a jobs record — where the rate is the question.

Real-world examples

  • •At its September 2013 product event Apple showed a chart of cumulative iPhone sales rising steeply since 2007; analysts pointed out that the quarterly sales figures, which the company also possessed, showed growth slowing, which the cumulative curve could not display.
  • •Startup investor guidance, including a widely circulated 2015 Andreessen Horowitz note on metrics, warns founders and investors against cumulative charts of users, downloads or revenue in pitch decks precisely because they look like growth regardless of whether growth is happening.
  • •Administrations of both parties report “jobs created since taking office” as a cumulative total that rises in any month with net hiring; the figure was used by the Obama White House after 2010, the Trump White House after 2017 and the Biden White House after 2021, and in each case it continued to rise through months in which the pace of hiring slowed.
  • •Cumulative COVID-19 case charts in 2020 were an honest measure of total burden, and were also used after local peaks as evidence that “cases are still rising”, when the daily series showed the outbreak receding.

Ethical guidelines

Where the line is

A cumulative chart is legitimate when the total is the quantity that matters — installed base, funds raised toward a goal, cumulative emissions — and the per-period series is shown or available; it becomes a trick when the audience's question is about the rate and the cumulative form was chosen because the rate has turned down and the sum still rises.

  • ●When you show a cumulative series, show the per-period series beside it or say in the caption what the current rate is and how it compares with earlier periods.
  • ●Choose cumulative form only when the total is what the audience needs to know, and say so; do not choose it because the rate is unflattering.
  • ●Label the chart “cumulative” prominently, not in a footnote.
  • ●Do not describe a rising cumulative curve as “growth” if the underlying rate is falling.

How to defend against it

  • ►Check whether the label says cumulative, total or “since”; if it does, ask for the per-period numbers, which is what a rate question needs.
  • ►Read the slope, not the height: a cumulative line that is bending toward flat is a rate that is falling.
  • ►Ask what last period's figure was compared with the same period a year earlier; a presenter with a cumulative chart and no answer to that question chose the chart for a reason.
  • ►Redraw a few points as period-by-period differences on paper; the trend usually appears in under a minute.

References

  1. Cairo, A. (2019). How Charts Lie: Getting Smarter about Visual Information. W. W. Norton
    Cumulative curves as a way to hide a declining rate, with corporate and political examples.
  2. Tufte, E. R. (2001). The Visual Display of Quantitative Information (2nd ed.). Graphics Press
    The general standard that a graphic should show the data variation the audience needs, not a transformation chosen for its shape.
  3. Wainer, H. (1984). How to display data badly. The American Statistician, 38(2), 137-147
    Transformations and chart forms that obscure the change the reader is looking for.
Last reviewed
Suggest a correction

Detect Cumulative Graph Trick in any text

Paste any message, email, or article into our free Manipulation Detector to see if Cumulative Graph Trick or other techniques are being used on you.

Try the Detector FreeCreate Free Account