The bathtub that didn’t get a single rubber duck

A pale blue bill-insert card on a deep teal background with a few bubble outlines. The masthead reads “The Drip Sheet · from Puddleford Water & Sewer” on the left and “Your October bill insert” on the right. The headline reads “Where your home’s water goes down the drain”, and the subhead says the average household sends about 130 gallons a day to the treatment plant, “one rubber duck at a time”. A tilted key at top right shows one yellow rubber duck “= 10 gallons a day”. Below are eight rows, each with a label, a row of whole rubber ducks and a total: Toilet, three ducks, 30 gal; Faucet, three ducks, 30 gal; Shower, three ducks, 30 gal; Clothes washer, two ducks, 20 gal; Leaks, two ducks, 20 gal; Bath, Other and Dishwasher each read “— less than a duck” in grey italics, with no ducks. A round yellow sticker on the right says “It’s a three-way tie! Toilet, tap and shower drain 30 gallons each”, and a dashed white note beneath it says “Bath, dishwasher & the rest: less than a duck. Don’t give them a second thought!” A footnote says the figures are average indoor use per single-family household from the Water Research Foundation’s Residential End Uses of Water, Version 2 (2016), executive report, Figure 1, explains that “Other” is evaporative cooling, humidifiers, water softeners and uncategorised indoor use, and says the insert is a demonstration drawn by Misleading Charts: the utility, its insert and its captions are invented, and the eight household figures are the study’s. — Showing the misleading chart

A cream page, kicked “The same eight numbers, unrounded · average indoor use per single-family household · gallons per day” and headlined “Rounded to whole ducks, the toilet tied the faucet and 10.6 gallons a day vanished from the picture.” A standfirst says a pictogram can only draw whole icons, so at 10 gallons a duck every row was rounded to the nearest 10, which means each row could be off by 5 gallons and each gap between rows by 10; the top five uses sit 0.1 to 5.6 gallons from their neighbours, so the rounding decided which rows tie and which get a whole duck between them, and it emptied the bottom three. The left panel, “The same ducks, cut to the gallon”, redraws the pictogram with the last duck in each row cut where its ink reaches the fraction, each cut marked with a thin cut line and a label: Toilet 3.26 ducks, Faucet 2.70, Shower 2.69, Clothes washer 2.20, Leaks 1.78, Bath 0.44, Other 0.40 and Dishwasher 0.22, the last three as slivers of a duck. The right panel, “What each row was rounded to”, is a dot plot on an axis ticked 0 to 30 gallons, with a key: a solid dark teal dot marks each actual value and a hollow orange ring marks what the ducks drew, joined by a short orange line. A table to its right lists actual, ducks said and off by: Toilet 32.6, 30, −2.6; Faucet 27.0, 30, +3.0; Shower 26.9, 30, +3.1; Clothes washer 22.0, 20, −2.0; Leaks 17.8, 20, +2.2; Bath 4.4, 0, −4.4; Other 4.0, 0, −4.0; Dishwasher 2.2, 0, −2.2. Three notes run along the bottom. “Ties that aren’t” says the toilet’s 32.6 gallons is 5.6 more than the faucet’s 27.0, about 21% more, yet drawn identical; leaks at 17.8 and the clothes washer at 22.0 tied too; and the shower at 26.9 and washer at 22.0, 4.9 gallons apart, got a whole duck between them. “Rows that vanish” says bath 4.4, other 4.0 and dishwasher 2.2 gallons make 10.6 a day, 7.7% of indoor use, about 3,870 gallons a year, all drawn as nothing; that the insert’s “about 130 gallons” is the 13 ducks counted back up; and that the eight figures add to 136.9. “Drawing it straight” says to trim the last icon to its fraction or choose a unit no bigger than the smallest gap that matters, and if the icons must stay whole, to print the number under each, as the study’s own figure does. A footnote credits the Water Research Foundation’s Residential End Uses of Water, Version 2: Executive Report (DeOreo, Mayer, Dziegielewski and Kiefer, April 2016), Figure 1, notes the report’s headline indoor figure is 138 gallons per household per day, explains the “Other” category, and says the drawing is ours and the bill insert it corrects is our invention. — Showing the misleading chart

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A water-bill insert we invented counts a household’s daily indoor water use in rubber ducks, 10 gallons a duck, and only ever draws whole ducks. The toilet, the faucet and the shower all get three, so the toilet’s 32.6 gallons ties the faucet’s 27.0. The bath, the dishwasher and “other” get none, which leaves 10.6 gallons a day, 7.7% of indoor use, off the picture.

Water Research Foundation, Residential End Uses of Water, Version 2: Executive Report (W. B. DeOreo, P. Mayer, B. Dziegielewski and J. Kiefer, April 2016), Figure 1, “Indoor household use by fixture”: average indoor use per single-family household, gallons per day, measured by flow-trace metering. The bill insert, the utility and both drawings are ours., 2016Added October 17, 2026

01The claim

Toilets, faucets and showers each send the same 30 gallons a day down a household’s drain, and the bath and the dishwasher add so little that they are not worth a second thought.

02The trick

Every duck is honest about its own 10 gallons, and the eight figures behind them come from flow-trace metering of 762 single-family homes in the US and Canada. The catch is that a duck can only be drawn whole. The insert never trims the last one, so every row is rounded to the nearest 10 gallons before it reaches the page, and each row can be off by up to 5 gallons with nothing to say which way, so the gap between any two rows can be off by up to 10. In this data that is bigger than every difference among the top five rows. The toilet’s 32.6 gallons rounds down to three ducks and the faucet’s 27.0 and the shower’s 26.9 round up to three, so the largest indoor use, about a fifth more than the faucet, comes out in a three-way tie. Leaks (17.8) round up and the clothes washer (22.0) rounds down, so they tie too. The washer and the shower are 4.9 gallons apart, and that gap gets a whole duck. Bath (4.4), “other” (4.0) and dishwasher (2.2) all fall under half a duck and are drawn empty, and the sticker turns that into advice. And because ducks can be counted, the error travels into the total: the insert’s “about 130 gallons a day” is just the 13 ducks counted back up, while the eight figures add to 136.9. (Puddleford Water & Sewer, its insert and its stickers are our invention; the figures are the Water Research Foundation’s.)

03The fix

The redraw keeps the ducks but trims the last one in each row to its true fraction, cut where the duck’s ink reaches that share of its area, so the toilet gets 3.26 ducks, the faucet 2.70 and the dishwasher a sliver of 0.22. Beside it, a dot plot marks each real value next to the round number the insert drew, so every row’s rounding error is visible, from 2.0 gallons for the washer up to 4.4 for the bath. The ranking the study reports comes back: toilet first, then faucet and shower nearly level, then the clothes washer and leaks. The three blank rows come back as 10.6 gallons a day, 7.7% of indoor use, about 3,870 gallons a year per household, which is not nothing. If icons have to stay whole for style, do what the study’s own figure does: draw one icon per item and print its number underneath. Then the icons are decoration and the numbers carry the data. A pictogram is fine for showing that a toilet drains more than a dishwasher. It cannot settle a 5.6-gallon question with a 10-gallon duck.