Axis crimes

Uneven intervals

1990, 1995, 2000, 2004, 2006, 2007 — evenly spaced.

a.k.a. irregular binning · elastic time

Plot irregular time steps at regular spacing and you silently stretch some periods and compress others. Slopes become fiction: a decade and a single year occupy the same width, so the “acceleration” is typography.

How to spot it

Read the x-axis labels: do equal gaps represent equal amounts of time?
Bins like 0–18, 19–25, and 26–64 drawn at the same width.

The fix

Position values where they actually fall. If bins must vary, their widths should vary with them.

In the gallery

Dark navy briefing slide, masthead “Facilities briefing · US public schools · Enrollment size of school · School year 2021–22 · Census · not a sample”, headlined “Six in ten American public schools enroll fewer than 500 students”. A standfirst says this is a census rather than a survey — every public elementary and secondary school in the fifty states and the District of Columbia files to the federal Common Core of Data, 99,239 of them in 2021–22 — and that the publisher’s size distribution runs over the 95,839 that reported an enrollment above zero, the other 3,400 having reported none, those 95,839 schools holding 49,089,640 students between them. It adds that the axis starts at zero, every band is plotted at the publisher’s own boundaries, nothing is smoothed, indexed, annualized or rebased and there is no second axis, and that on that count the commonest school in the country holds 300 to 399 students, 61.5% of schools enroll fewer than 500, 32.0% fewer than 300 and very nearly one school in ten — 9.96% — fewer than 100, while only 9.0% reach 1,000 students and 0.34% reach 3,000. The main panel, labelled “Share of public schools, by enrollment size · 2021–22 · axis 0 to 16% · every school counted once”, is a column chart of thirteen blue bars with gridlines at 0, 4, 8, 12 and 16 percent, each bar labelled with its value: Under 100 at 10.0, 100–199 at 9.4, 200–299 at 12.6, 300–399 at 15.3 picked out in gold as the tallest, 400–499 at 14.2, 500–599 at 10.9, 600–699 at 7.7, 700–799 at 5.2, 800–999 at 5.7, 1,000–1,499 at 5.1, 1,500–1,999 at 2.0, 2,000–2,999 at 1.5 and 3,000+ at 0.3. The x-axis is captioned “Enrollment size of school · percent of the 95,839 reporting schools in each band”. A table headed “The distribution as drawn” lists every band with its exact percentage of schools and the school count that percentage implies: 9.96 and 9,546; 9.41 and 9,018; 12.62 and 12,095; 15.35 and 14,711; 14.15 and 13,561; 10.88 and 10,427; 7.71 and 7,389; 5.18 and 4,964; 5.73 and 5,492; 5.11 and 4,897; 2.02 and 1,936; 1.53 and 1,466; 0.34 and 326. A second table, “Small schools dominate the count”, gives cumulative shares — fewer than 100 at 9.96%, fewer than 200 at 19.37%, fewer than 300 at 31.99%, fewer than 500 at 61.49%, fewer than 800 at 85.26%, 1,000 or more at 9.00%, 2,000 or more at 1.87% and 3,000 or more at 0.34% — and notes beneath that the median school, the fiftieth of every hundred counted from the smallest, falls in the 400–499 band, and that mean enrollment per reporting school is 512.2 students. Down the right-hand side a card carries the figure “61.5%” over “Public schools enrolling fewer than 500 · 2021–22” and “Modal band 300–399 · mean 512.2 students”. A card headed “Read-out for the facilities board” says America is a nation of small schools, that the median school sits in the 400–499 band and the average school holds 512.2 students, so a site of roughly 500 is the country’s normal case rather than its small case. A “Planning note” card says a staffing model, a counselling ratio and a per-site technology package specified for a school of about 500 will fit the majority of American sites without modification, and that large-campus provision is the exception since fewer than one site in ten reaches 1,000 students. A card headed “Why a census, and what its base is” says these are not estimates, that every public school files to the Common Core of Data so there is no sample and no margin of error and the percentages are counts, and that the publisher computes them over the 95,839 schools reporting enrollment above zero while the 3,400 reporting none are outside the distribution. A “What we did not do” card lists a zero-based axis, every band plotted at the publisher’s own boundaries, nothing smoothed, indexed, annualized, projected or rebased, no second axis, no log scale and no break, and “one year, one country, one unit”. A “Basis of measurement” card names NCES, Digest of Education Statistics 2022, Table 216.40, with underlying data from the NCES Common Core of Data, 2021–22. Five ticked boxes run along the foot: “Zero-based axis”, “Every reporting school counted”, “Publisher’s own size bands”, “Census, not a sample” and “Base stated”. A footnote gives the source, notes that percentages are of the 95,839 schools out of 99,239 reporting enrollment above zero and sum to 99.99 through rounding, that the school counts in the table are those percentages applied to that base, and says the slide is a demonstration drawn by us in the manner of a facilities briefing, that the board, the read-out and the planning note are invented, and that every figure behind it is real.

$Pictogram titled “The Shrinking Family Doctor,” redrawn after the 1979 Los Angeles Times original: three doctor figures for 1964 (27%), 1975 (16.0%) and 1990 (12.0%), each scaled in both height and width so the 1990 doctor is a tiny fraction of the first, with the three years spaced evenly despite 11- and 15-year gaps$

The family doctor who shrank in two dimensions

The area illusion Uneven intervals

Uneven intervals

How to spot it

The fix

In the gallery

The 61.5% of schools that hold 32.7% of the children

The year that was seven months long

The peak-copper wall built entirely of tick marks

The marathon record that fell like clockwork

The family doctor who shrank in two dimensions