Six in 316

The quiz had come back on Monday afternoon, face down, and he had turned it over in the large flat room in the glass building with a hundred and twenty other people turning theirs over round him, and looked at it.

58.

It was written in red, in the top right-hand corner, in a small round hand, and underneath it, smaller, there was a sentence.

Variance is your friend!

With an exclamation mark.

The woman who taught Statistics was perhaps five feet tall, and wore enormous earrings, and taught a hundred and twenty people at once standing in front of a screen with a pointer, and she had said variance is your friend on the first day of the semester and every day since, in the tone of a woman introducing two people at a party who she is sure will get on.

They had not got on.

He had looked at the fifty-eight for some time. Then he had folded the quiz in half and put it in the back of his notebook, and walked back across the campus in ninety-seven degrees, and not looked at it again until dinner, when he had put it on the table in the dining hall by the window, beside Sam’s tray, face up.

Sam had looked at it over his round glasses.

He had looked at it for a long time, as a man looks at an invoice that has been paid twice, and then at Frederick, and then back at the fifty-eight; and he had put down his fork, and taken the pencil out from behind his ear, and opened the notebook, and turned to a clean page.

“Six o’clock,” said Sam. “Three-sixteen.”

“Tonight?”

“Tomorrow.” Sam wrote something at the top of the clean page. “In the morning.”

---

At a minute to six he knocked on 316.

He had got up at a quarter to, at the same instant as the lamp on the desk by the door, and said “I’m going to Sam’s,” and Alexander had looked at him from the bed by the door, sitting up, with the sheet folded down to his waist in its straight line, and said “At six?” and Frederick had said “Statistics,” and Alexander had considered it and said “Then the shower is mine at five forty-eight,” in a voice of quiet and enormous satisfaction, and Frederick had gone out into the corridor in his T-shirt with his notebook and a pencil and left him to it.

Sam opened the door before the second knock.

He was dressed. He was always dressed. Frederick had never in a year seen Sam not dressed, at any hour, and had come to think it possible that he slept in his shirt, with the notebook on his chest. The room behind him was dark except for the lamp on his desk, under the poster of the federal tax brackets, which was the only thing on the wall and had been since last August, held up by its four drawing pins.

On the other bed there was a shape under the cover, and on the shape, over the place where its head would be, a pillow.

“Rhys?” said Frederick.

“Asleep,” said Sam.

“Under a pillow?”

“He says the lamp gets in.” Sam stood aside. “He says statistics gets in as well. Through the pillow.” He looked at the shape. “He’s not wrong.”

From under the pillow, very faintly, Rhys said, “I can hear you,” and then, after a moment, “Morning, sir,” and then nothing.

---

There were two chairs at Sam’s desk. Sam had brought the second from the lounge, the night before, Frederick realised, and carried it up the forty-five steps, because there had only ever been one; and he sat Frederick in Sam’s own chair, under the tax brackets, where Frederick did the box every morning, and took the lounge chair himself, beside him, at the corner of the desk, and opened the notebook.

“You don’t need the textbook,” said Sam.

“It’s the textbook.”

“It’s got the wrong numbers in it.” Sam turned the notebook round so that Frederick could see it. “It’s got the heights of four hundred men in Leeds in 1950. You don’t care about the heights of four hundred men in Leeds in 1950.”

“No.”

“Nobody does. That’s why you got fifty-eight.” Sam put his finger on the page. “So we’re not doing men in Leeds. We’re doing the hall.”

The page had a heading, at the top, in pencil, in Sam’s small square capitals, underlined.

FRED (SUNS, MISSING), BY WEEK, SINCE 17 AUG.

And under it, in a column:

4 2 3 1 5

“You’ve been counting the suns,” said Frederick.

“I’ve always counted the suns,” said Sam. “Since last August. Callum puts a new one up every time and I write it down.” He did not seem to think this required defence. “That’s five weeks. Thursday to Wednesday. That one” (he touched the 1) “is the week you were in Stockholm.”

“Somebody still took one?”

“Somebody always takes one,” said Sam. “Even when you’re not here. That’s important. We’ll come back to it.” He laid the pencil on the desk. “Mean.”

“Add them up.”

“Add them up.”

“Four and two is six. And three is nine. And one is ten. And five.” Frederick looked at it. “Fifteen.”

“And?”

“Divide by five.”

“Why five?”

“Because there are five of them.”

“Good,” said Sam. “Three. The mean is three. On average, three people a week take your name off a door.” He wrote mean = 3 under the column. “Median.”

“The middle one.”

“Put them in order first.”

Frederick wrote them out again in order, on the page, in his worse hand. 1, 2, 3, 4, 5.

“Three,” he said.

“Three,” said Sam. “Same. That happens when it’s even. When nothing’s weird.” He turned a page. “Now we’re going to make something weird.”

---

The next page said GLACIER (EMPTY), 312, BY DAY, LAST WEEK.

2 1 3 2 2 0 9

“Tyler,” said Frederick.

“Tyler,” said Sam. “He comes at four and leaves at ten to six. Your roommate’s got it on a programme, so I asked him for the numbers, and he had them.” He looked at the column with something like admiration. “He’d counted. He’s got a column as well. In German.”

“What’s the nine?”

“Sunday. Brayden’s mother came from Mesa with a cooler.” Sam touched the 0. “Saturday he didn’t come. He went to the game with Brayden. He said Brayden talked through the whole fourth quarter about a different game.” He looked up. “So. Mean.”

Frederick added them up. It took him longer. He got twenty, and then nineteen, and then nineteen again.

“Nineteen. Divided by seven.” He looked at it. “Two and a bit.”

“Two point seven one. And median?”

He wrote them out in order. 0, 1, 2, 2, 2, 3, 9.

“Two.”

“Two,” said Sam. “So which one’s true?”

Frederick looked at the two numbers.

“The median,” he said slowly. “He drinks about two a day. The nine’s just Brayden’s mother.”

“That’s it,” said Sam, and for a moment, under the lamp, something happened at the corner of his mouth, very far back, and was put away. “That’s the whole of chapter three. The mean moves for one Sunday. The median doesn’t care about Sunday.” He wrote it at the bottom of the page in capitals and underlined it. THE MEAN MOVES FOR ONE SUNDAY. “If you ever want to know what something’s really like, ask for the median. If somebody gives you the mean, ask them if there was a Sunday.”

From under the pillow on the other bed, Rhys said, “That’s actually really good,” and was asleep again.

---

“Variance,” said Sam.

He turned back to the first page, the suns.

“She says it’s my friend,” said Frederick.

“She’s right.” Sam put the pencil under the column. “Variance is how far everything is from the mean. On average. So you can tell if the mean’s any good.” He drew a line down the right-hand side of the column, and beside each number wrote another one. “Four. That’s one more than three. Two. That’s one less. Three. That’s nothing. One. Two less. Five. Two more.”

+1 -1 0 -2 +2

“Add them up,” said Sam.

“Nothing.”

“Always nothing. That’s why you square them.” He wrote again, beside each. 1, 1, 0, 4, 4. “Add those.”

“Ten.”

“Divide by four.”

Frederick looked at him.

“There are five of them.”

“Divide by four.”

“Why four?”

“Because you used the mean,” said Sam. “You worked out the mean from these same five numbers, and then you measured them from it. So you’ve spent a bit of the information already. On the mean. You’ve got one less left.” He wrote n minus 1 in the margin, small. “It’s called a degree of freedom. You lost one.”

“Where did it go?”

Sam considered this.

“Into the mean,” he said.

Frederick looked at the five numbers, and the three under them, for a long time, and found that he was thinking about a box of forty pages that came at a quarter to seven, and the question of where anything went once it had been initialled.

“Two and a half,” he said.

“Two point five. That’s the variance. Take the square root, because you squared them, and you get back to suns.” Sam wrote. “One point five eight. That’s the standard deviation. That’s the thing on the quiz. Question six. You left it blank.”

“I didn’t know what it was.”

“Now you do,” said Sam. “It means: three suns a week, give or take one and a half. Most weeks, somewhere between about one and about five.” He looked at the column. “Which is what happened. So the mean’s all right. You can use it. If somebody asks how many people steal your name, you can say three, and you won’t be lying much.”

---

There was a second column on the first page, to the right of the first one, that Frederick had not noticed, because it was very short and very neat and in a different heading.

ALEX (SUNS, MISSING), BY WEEK.

0 0 0 0 0

He looked at it.

“Nobody’s taken it,” he said.

“Not once.” Sam did not look at the column. He looked at the tax brackets. “Mean, nothing. Median, nothing. Variance, nothing. Standard deviation, nothing.”

“Because nobody knows who he is.”

“Because nobody knows who he is,” said Sam. “Yet.” He put the pencil down, parallel to the edge of the notebook, and looked at it, and moved it slightly so that it was not. “It’s the most predictable thing on the floor. You could set your watch by it. Zero, every week.” He was quiet for a moment. “In accounting, when a number doesn’t move at all, for weeks, you go and look at it. Because real numbers move. A number that never moves is usually somebody being very careful.”

Frederick looked at the column of noughts.

“Or nobody taking it,” he said.

“Or nobody taking it,” said Sam. “Usually.” He closed the notebook. “That’s not statistics. That’s just me.”

---

They did the steps at twenty past six.

Sam had a third page, STEPS, GROUND TO 3RD, BY RESIDENT, which he had compiled over a week by asking every person on the third floor, at the top of the stairs, without explanation, how many there were, and writing down what they said; and he had twenty-six answers, of which eleven were forty-five, nine were forty-four, four were I don’t know, dude, one was seventy-nine, which Sam had crossed out as a temperature, and one, from the boy in flip-flops who sang in the shower, was too many.

“What’s the mean?” said Frederick.

“There isn’t one,” said Sam. “That’s the lesson. You can’t take the mean of I don’t know, dude.” He tapped the forty-fours and the forty-fives. “And you can’t take the mean of these either. Forty-four and a half isn’t a number of steps. There’s no half a step. There’s the little one on the first landing, and either you count it or you don’t.” He looked at the page. “That’s not a variance. That’s a disagreement.”

“Which one does he say?”

“Your roommate? Forty-five.” Sam did not look up. “He counts the little one. He counts everything.”

“And you?”

Sam considered it for a long time, with the pencil.

“I don’t take sides,” he said, “in a dispute about data.”

---

At twenty to seven Sam stood up, and put the notebook in his shirt pocket, and took the grey backpack with the broken zip off the hook on the back of the door.

“Box,” he said.

Frederick went to the window of 316 while he was gone, and stood at the edge of the blind, and watched Sam come out under the arcade with the backpack on one shoulder and cross the road in the half-light, between the cars, to the low building with the dentist’s sign; and above the dentist’s, on the second floor, the blind in the third window moved, an inch, and stayed.

Behind him the shape under the pillow turned over.

“Is it over?” said Rhys, from under the pillow.

“Nearly.”

“Did you get it?”

“Some of it.”

“I got a ninety-four,” said Rhys, still from under the pillow, in a voice of great sorrow. “Last year. In Statistics. I don’t know what a standard deviation is either.” A pause. “Don’t tell Sam.”

“I won’t.”

“He knows,” said Rhys, and went back to sleep.

At a quarter to seven the box came up the forty-five steps in the grey backpack, and Sam put it on his own desk, and Frederick sat in Sam’s chair under the federal tax brackets with the red box open in front of him and forty pages about the Realm in it, and did them, and initialled each one in pencil, small, in the top right-hand corner; and at seven, through the wall, he heard the single knock on 312, and the door, and a few words in German, low, and the door shutting.

There was a paper in the box from the Treasury, about a trade figure for the second quarter. He read it twice. It had a mean in it, in a table, and no median, and he looked at it for a long time, and found himself wondering whether there had been a Sunday.

He initialled it anyway. It was not his to ask. It was the Treasury’s.

But he wrote, very small, in pencil, in the margin, where nobody but the Household would see it, median?, and then sat and looked at it, appalled, as though somebody else had written it.

---

By lunch he had forgotten what a standard deviation was.

He knew he had known. He could remember the lamp, and the tax brackets, and the column of suns, and the n minus 1 in the margin, small, and the degree of freedom that had gone into the mean; and he could remember that it was the square root of something, and that the something was two and a half. But when Alexander asked him, across the table by the window in the dining hall, with the butte a mile off and the waffle iron going and the ABC on the television with the sound down, what a standard deviation was, because it had come up in the reading for the Executive, in a table about Prime Ministers’ majorities, he opened his mouth, and found that there was nothing in it.

“It’s,” he said. “It’s the. You square them.”

Alexander waited.

“And then you lose one,” said Frederick. “Into the mean.”

Alexander considered this for some time, with his fork laid down parallel to the edge of the tray.

“I see,” he said, in the voice of a man who does not, and has decided that it would be unkind to say so.

---

Statistics was at two.

The woman with the enormous earrings stood in front of the screen in the glass building with her pointer and asked a hundred and twenty people a question about house prices in Flagstaff, and the mean, and a man who owned a hotel; and nobody answered; and Frederick, in the fourteenth row, heard himself say, quite loudly, “Ask for the median.”

She looked along the rows at him.

“Why?”

“Because of the hotel,” said Frederick. “The mean moves for one Sunday.”

There was a pause in the room.

“I’ve no idea what the second part means,” said the woman with the earrings, “but the first part’s correct.” She beamed at him, enormously, as though he had introduced her to somebody at a party. “Variance is your friend!”

He did not tell her that it had gone. He sat in the fourteenth row with the median and nothing else, like a man who has saved one thing from a fire and is not sure it was the right one.

---

At ten that night there was a page under the door of 312.

It had been torn out of the notebook, neatly, along the edge, with a ruler, and pushed under the door while he was on the step with his mother, and it was lying on the floor just inside when he came in, face up.

It was the first page. The suns. The column of five numbers, and the mean, and the median, and the five small numbers beside them with their pluses and minuses, and the squares, and n minus 1, small, in the margin, and at the bottom, in Sam’s square capitals, underlined: STANDARD DEVIATION = 1.58 (SUNS). ASK ME AGAIN THURSDAY. S.

And on the right, the short neat column.

0 0 0 0 0

He pinned it to the cork board over the desk under the window, with one drawing pin, at the height of his eyes, so that it would be the first thing he saw in the morning.

At twenty-nine minutes past ten Alexander got up from the bed by the door, and crossed first to the window desk, and looked at the page on the cork board for a while, with his hands behind his back, as a man looks at a picture in a gallery that has been hung slightly too high.

He read the column on the right.

“That is correct,” said Alexander.

He went to the box by the door, and looked at the number in it, and did not touch it, and got back into bed, and put out the lamp; and Frederick lay on his back in the bed by the window in the dark, with the page on the cork board over the desk, which he could not see in the dark, and tried, for a long time, to remember what you did after you squared them, and could not, and remembered instead, quite clearly, Sam’s voice under the lamp at half past six saying that a number that never moved was usually somebody being very careful.