← Errata: Where the Bars Begin
The Commons Year · The case · ages 15-18
1. The Stub
The hammer rang once. A spark jumped off the anvil and did not go out. It waited. They followed.
The March issue of the Green Gazette had a chart on the front page, and Tara was proud of it. The Gazette did not usually have charts. It had photographs, and the crossword, and once a drawing of the headteacher's dog. But Jun in Year 10 had learned to make charts in his computing lessons, and he had wanted to try one on a real story.
The story was about the school library. Jun had asked Mr Adebayo, the librarian, whether he kept a count of visitors, and Mr Adebayo had said of course he did. Every pupil who came in tapped their card on the reader by the door, and the machine kept a log. Jun had asked for last autumn's total and this autumn's. Then he had typed the two numbers into a spreadsheet and pressed the button that made a chart.
It looked very professional. Two blue bars, side by side, with a neat axis up the left-hand side and the numbers printed on top. Last autumn's bar was tall. This autumn's bar was a stub, a quarter of the height of the other one. Above them ran the headline in thick black letters:
LIBRARY VISITS PLUNGE
By Wednesday a governor had stopped Mrs Hallam in the car park to ask about it. By Friday the chart had been photographed and put on the parents' group, with three angry faces and a question about what the library was for if nobody went.
On Saturday there were two letters in the Gazette box.
The first was from Mr Adebayo himself, written on the back of a library reminder slip, in small, careful capitals.
The governors met on Thursday, it said. They have your front page. They are now talking about closing the library on Thursday evenings, which is when the Year 11s come in to revise and the Year 7s come in to read because their buses are late. I have run this library for fourteen years. I would like to understand what the picture is saying, because it is not what I see when I open the door.
The second letter was in purple felt pen, on a page from a reading journal. It was from Ffion in Year 7.
I read that the library is going down, it said. I didn't want to have overdue books if it closed, so I took them all back. I hadn't finished the dragon one. Is it closing? I didn't want it to.
Tara pinned both letters to the board above the back table at the Whetstone café. She looked at the purple writing for a long time.
She had been proud on Tuesday. Now she was uneasy, and she did not know why yet.
2. A Crop Is a Choice
"I was going to say every number on it is right," Tara said.
She had brought the letters to the back table. Danya was there, eating toast and drawing a map of a made-up island in the margin of his homework. Across from him sat Uncrop, who took the Gazette's photographs and had once refused to hand one in until the editor had seen the whole roll. Uncrop always asked to see the whole picture. It was a joke at the Gazette, and also it wasn't.
"I was going to say it like this," Tara said. "Jun took both numbers straight from the library's own machine. Nothing is made up. The bars are the right numbers. I can write back to Mr Adebayo and Ffion and say so."
She already had the sentence half written in her head. Thank you for your letter. The figures in our chart were supplied by the library.
It felt good. It felt like the end of the conversation.
Uncrop picked up the front page and held it at arm's length, the way you look at a photograph to see what the photographer has done.
"A crop is a choice," said Uncrop. "Every picture is cut off somewhere. Somebody chose where to cut it. Before we answer anybody, tell me what's outside the frame."
"It's a chart," said Tara. "It hasn't got a frame."
"Everything has a frame," said Uncrop. "Look at the edges."
"Says who?" said Danya, through toast.
"Says Ffion," said Uncrop, and tapped the purple letter. "She looked at this picture and she saw a library closing. Mr Adebayo opens the door every morning and he doesn't see that. One of them is looking at the picture and one of them is looking at the room. I'd like to know why they don't match."
Tara opened her mouth. Then she shut it again.
"How do we know which one's right?" Danya asked.
Nobody knew. That was the problem.
3. The Log
Deed came in at eleven, with a carrier bag of library books and a printout of the council's spending on street lights. Deed read council minutes for fun. She kept every planning application on her phone, sorted into folders. She had once found a mistake in the town budget on page two hundred and nine, and she had never stopped being pleased about it.
Tara showed her the front page and the two letters.
"Where's the log?" Deed asked.
"Jun's got it. It's just two numbers."
"Go to the original document," said Deed. "The chart is a picture of the numbers. I want the numbers themselves, where they were first written down. A summary of a summary drifts, and a picture of a number is a kind of summary."
Tara texted Jun. Jun replied in two minutes, with a photograph of a printout from the library's card machine. It had the school's name across the top, the dates of each term, and a total at the bottom of each column. Mr Adebayo had initialled it in green ink.
Deed turned the phone round so everyone could see.
Autumn term, last year: 1,180 visits.
Autumn term, this year: 1,120 visits.
"Show me the source, then," said Danya, leaning in. "Is that it?"
"Read it where it was first written down: that's it," said Deed. "Jun copied them exactly. Those are the numbers on the chart. Eleven hundred and eighty, and eleven hundred and twenty."
"So the chart's right," said Tara.
"The numbers are right," said Deed. She took a pencil from behind her ear and did the subtraction in the margin of the street-lights printout. "Sixty fewer visits this autumn than last. That's real. The library really is a bit quieter."
"How much is a bit?" said Danya.
Deed did it on her phone. "Sixty out of eleven hundred and eighty. About five per cent. One visit in twenty."
Tara looked at the front page again. Last year's bar towered. This year's was a stub.
"That doesn't look like one in twenty," she said.
"No," said Deed. "It doesn't."
4. The Edges
Uncrop had already taken out a ruler. Uncrop carried one in a coat pocket, the way other people carried a pen, for measuring prints.
"Look at the edges," said Uncrop. "Not the bars. The line up the side."
Tara looked. Along the left-hand side of the chart ran the axis, with little numbers beside it in grey. The numbers went up in tens. At the top was 1,190. At the bottom, where the bars stood, it said 1,100.
Not zero. One thousand one hundred.
"What's outside the frame?" said Uncrop. "Everything from nought to eleven hundred. The spreadsheet cut it off, because that's what spreadsheets do when the numbers are big and close together. It zooms in on the tops. Somebody chose where to cut it, even if the somebody was a computer."
Uncrop laid the ruler against the bars.
"Last year's bar is drawn from eleven hundred up to eleven hundred and eighty," said Uncrop. "So it's eighty tall. This year's goes from eleven hundred to eleven hundred and twenty. Twenty tall."
"Eighty and twenty," said Danya. "That's four times."
"Four times," said Uncrop. "Your eye reads the length of a bar. That's the whole point of a bar. And these lengths say this year is a quarter of last year. The numbers on top say it's one visit in twenty fewer."
"Who checked that before it went on the front page?" said Danya. "That's mad."
"It's not mad. It's the button," said Uncrop. "Here. Show me the whole picture."
Uncrop took a pencil and drew the chart again on the back of a napkin, properly this time, with the axis starting at zero at the bottom. Two bars. The first went up to eleven hundred and eighty. The second went up to eleven hundred and twenty.
They were nearly the same height. You had to look carefully to see which one was shorter. This year's bar was about ninety-five hundredths of last year's.
"That's what Mr Adebayo sees when he opens the door," said Uncrop. "That's the room. The front page is a close-up of the very tops of two bars. A crop is a choice."
Tara stared at the napkin. Then at the front page. Then at the napkin again.
The numbers were right. The picture said something the numbers did not.
5. Per Pupil
Widen arrived with a takeaway hot chocolate and a calculator that he did not need. Widen wrote the Gazette's money pages. He kept a small notebook of what things cost, from a bus ticket to a bridge, and he could not hear a number without wanting to put another number next to it.
He read the front page, the letters, the log and the napkin, one after another.
"Compared with what, though?" said Widen. "Eleven hundred and twenty visits compared with what? Widen the view. How many people could have visited?"
"Everyone in the school," said Tara.
"And how many is that? Was it the same both years?"
Nobody knew. Danya looked it up on the school website, which had the numbers on the page for new parents. Last autumn there had been a thousand pupils. This autumn there were nine hundred and fifty.
"Why fewer?" said Tara.
"The new Year 7 is small," said Danya. "My cousin's in it. There are only five forms instead of six. Everyone says it's because they built the new school over by the ring road."
"One number on its own tells you almost nothing," said Widen. He did it on his calculator anyway. Eleven hundred and eighty visits, shared between a thousand pupils, was one point one eight each. Eleven hundred and twenty, shared between nine hundred and fifty, was one point one seven nine. Call it one point one eight.
"Compared with the number of pupils, it's the same," said Widen. "One point one eight visits each, both years. There are fifty fewer pupils in the school. Each of them is using the library exactly as much as last year's lot."
He wrote both in his notebook, side by side, and drew an equals sign between them.
"Is that a lot, or does it just sound like a lot?" Widen asked. "Sixty fewer visits sounds like a story. Fifty fewer pupils explains nearly all of it."
Tara looked from the log to the napkin to the notebook.
"Can I say one thing?" Tara asked. "So the front page was wrong?"
"Not wrong," said Uncrop. "Every number on it is true. It was drawn to look like more. And it was counted without asking how many people there were."
"And Mr Adebayo," said Widen. "Our chart makes his library look as if it's emptying. Per pupil, it's as busy as it was."
6. The Box
Attest came last, carrying the Gazette's red pen. Attest subbed every story before it went to print and drew a red circle round any number that did not have a name next to it. The March front page had come back with no circles on it at all, because every number did have a name next to it. Jun had been careful about that.
"Where did that number come from? Everybody could see the answer to that," said Attest. "The log. I checked. I didn't check where the bars began. I didn't think a chart could be wrong if the numbers were right."
"Nobody did," said Tara.
"Let me listen first," Tara said, before anyone could start explaining. She had learned that in the autumn, from the photo of the flooded underpass, and again last month, from the average Saturday. She took out a pad and wrote three headings across the top: what we printed, what the log says, what is missing.
Under the first she wrote a bar a quarter the height. Under the second she wrote 1,180 then 1,120, sixty fewer, about one in twenty. The third column stayed empty for a while. Then she wrote where the bars begin and, underneath, per pupil.
"Hm. So what does a clarification like this have to carry?" Tara asked.
"Every claim names its source," said Attest. "This one is the library's own log, so it says so. It has to say where the chart's axis started, at eleven hundred, not at nought. It has to carry the size of the fall in words people can picture, about one visit in twenty. And it should give the visits per pupil, because the school got smaller."
"Do we take the chart down? Say Jun got it wrong?"
"No," said Attest. "Jun's numbers are right, and he named his source. Put a name next to it, and say what the picture did. That's all."
"Hm. That's a lot for one box," said Tara.
"It's two sentences," said Attest. "Maybe three. And possibly a picture of a napkin."
Tara looked at Ffion's letter again, in purple pen. I hadn't finished the dragon one.
"I think we missed someone," Tara said slowly. "Jun. It was his first chart. If the box says the chart was misleading, everybody will think he made it up. He didn't make anything up. He pressed the button everybody presses."
Nobody answered at once.
"A correction names its source too," said Attest. "Who you name is your call. That's your bit."
7. Four People and a Pen
Mrs Hallam, who advised the Gazette and signed off every issue, came in at noon. Jun came with her, looking as if he wanted the floor to open. Mr Adebayo came ten minutes later, in his coat, carrying a box of returned books he had not had time to put back. Ffion did not come. She had sent a message through Danya, whose cousin was in her form, to say she was too embarrassed.
Jun spoke first.
"The numbers are right," he said. "I checked them twice, and Mr Adebayo initialled the printout. And it did go down. If I'd started the chart at nought, the two bars would look exactly the same, and then people would say nothing had happened. Something did happen. Sixty fewer visits is sixty fewer visits. You'd have told me off for hiding it, Tara."
It was the strongest version of his argument, and he was right that the fall was real.
Mrs Hallam spoke next.
"I'm not going to pretend I didn't like that headline," she said. "Libraries all over the country are being cut. If we want people to care about ours, they have to notice it. A chart with two bars the same height isn't a story. Nobody would have read it."
Then Mr Adebayo put his box of books down on the table.
"I am not asking you to say the library is perfect," he said quietly. "It isn't. It's a bit quieter on Mondays than it used to be, and I don't know why. I am asking you to understand what the picture did. The governors looked at that stub and decided that nobody uses the library. On Thursday evenings forty children come in. If they close it, those forty children have nowhere to go until their bus comes."
"I didn't mean that," said Jun.
"I know," said Mr Adebayo. "You didn't. A picture did."
Then Danya read out Ffion's message, because she had asked him to.
I don't want to be in the paper. I just want to know if I can take the dragon book out again. And if it's closing.
Nobody said anything for a while.
Mrs Hallam took the corrections box out of her bag. It was a small grey panel at the bottom of page two, with a border round it and room for a few lines. She had used it six times that year. She set it on the table in front of Tara, with the March front page beside it.
On the table in front of Tara were Jun's printout from the library machine, with its green initials. There was Uncrop's napkin, with two bars nearly the same height. There was Widen's notebook, with one point one eight on each side of an equals sign. There was Attest's list of what the box had to carry. And there were three letters: one on a library reminder slip, one in purple pen, and one on Danya's phone, from a girl who hadn't finished the dragon book.
"You're the editor," said Mrs Hallam. "What does it say?"
She handed Tara the pen.
Tara looked at the empty box.
(Write the line Tara prints in the corrections box.)
The spark dimmed to a warm dot and settled back on the anvil. The Green was just the Green again.
Back on the Green
That week Lan, who was seven, came home and said her sunflower had grown loads.
Danya asked how much. Lan showed him the photo on her grandmother's phone, zoomed right in on the top of the stalk, where a new leaf had come.
Danya asked to see the whole plant. Lan zoomed out. The new leaf was a tiny thing at the top of a very tall flower.
Lan looked at it for a while and said it still counted.
Danya said it did count. He just wanted to see where the flower began.
Afterword. The idea in this case is the truncated axis. A bar chart shows each value by the length of its bar, so its axis should start at zero. When the axis starts higher, at 1,100 in this case, only the tops of the bars are drawn, and a fall of one in twenty can look like a fall of three quarters. Spreadsheets often do this on their own when the numbers are large and close together. A line chart can sometimes zoom in fairly if the axis is clearly marked, but a bar's length is its value. The second idea is the rate per person: when the number of people changes, divide by it before comparing. Good reporting says where a chart begins, gives the size of a change in words people can picture, and never takes a true number back. You can practise building charts and choosing their axes in DataForge, and putting a number next to another in NewsForge.
Saved. The next chapter will be here whenever you come back.
Who you met
- Uncrop An image is cropped; ask what sits outside the frame from NewsForge
- Deed Go to the original document, not a summary of a summary from NewsForge
- Danya a child of the Green Asks "how do we know?"
- Widen One number means little without something to compare it with from NewsForge
- Attest Every claim names its source, and a correction names one too from NewsForge
- Tara a child of the Green Listens longest, speaks last
Every recurring character has a short tune, so you can tell who is on stage before a word is said. The tunes play only when you tap, and the Reading Access sound switch turns them off.
The Honest Page
Which parts of this story are true, stretched or made up?
True
- A bar chart shows a value by the length of its bar. If the value axis starts above zero (a truncated axis), small differences are drawn as large ones, which is one of the commonest ways a chart misleads. Source
- In the case, 1,180 visits fell to 1,120, a fall of 60, about 5%. With the axis starting at 1,100 the bars are drawn 80 and 20 tall, four times apart. With 1,000 pupils and then 950, the visits per pupil are 1.18 and about 1.18.
- A rate per person (per capita) divides a count by the number of people, so that groups of different sizes, or the same group in different years, can be compared fairly. Source
Stretched
- In the case, the chart is redrawn and the question is settled in one afternoon. What we simplified: A line chart showing a small change over time is sometimes drawn with an axis that does not start at zero, and that can be fair if it is clearly marked. A bar chart is different, because the length of the bar is the value.
Made up
- The library, its log, Jun, Ffion, Mr Adebayo, the governors and the Green Gazette's March front page are made up. The idea of a truncated axis is real.