Too Far from the Average

By Bobby Neal Winters

Buster Williams was sitting in his Elementary Statistics class struggling not to go to sleep.  Sometimes he bit his lip, sometimes he slapped himself on the neck--a trick he’d learned while driving all night to get to Panama Beach--but nothing he did seemed to work.  The problem was at the front of the classroom: the Standard Deviation, or Dr. Bottlebutt as he was known in polite society.

Professor Bertram Bottlebutt, covered from head to foot with chalk dust, wrote one last equation on the board.  He turned for the first or second time during class and asked, “Are there any questions?

Twenty pairs of glazed eyes, Buster’s included, didn’t even blink in response. This was a trick considering he’d been drifting off to sleep before.

“In that case,” he said, “class dismissed.”

Buster felt a rush of adrenaline. His heart soared.  Existence was worth continuing again.

For the first time in an hour, the students in the room showed life. Notebooks were shut, slid into backpacks, and motions were made toward the door.

“Wait, wait, wait,” he called out.  It was something students had heard before.  Indeed several of them did passible imitations of Dr. Bottlebutt, and competed against each other with their “Wait, wait, waits”.

“I need to talk to ... uh... Williams and ... uh ... Young,” he said.

Buster, hearing this, uttered an expletive to himself.

Since being in Dr. Bottlebutt’s class, he’d gotten used to being called “Uh...Williams.” Everyone who took a class from Bottlebutt had the same first name. Students also worked uhs into their imitations of Dr. Bottlebutt.  This was a man who could give hour upon hour of lecture of mathematics composed entirely of abstruse equations on the blackboard without any notes at all but could remember Bob, Emily, or Buster.

The room emptied of students with the expressions of those who, having eaten their morning live frog, knew everything would be better for the rest of the day.  All but Buster and Young who remained.

“Uh...Young” was actually named Betty.  Buster had been sitting in a desk one behind and to the left all semester just because he wanted to be able to see her.  She was...gorgeous. Everything that nature equipped young women with to get the attention of young men was present in Betty not in abundance but in perfect proportion.  And everything was presented in such a way that Buster could find no way to ignore.  As he stood, working on an inventory of Betty starting at her ankles, working up her calves to her thighs...

“Mr. Williams,” came Dr. Bottlebutt’s voice. “Could I please have your attention?’

“Uh...” oh God it must be catching he thought, “Sorry.”

“I was saying my assistant lost your and Miss Young’s grades,” said the professor, seeming quite chagrinned. “I always put the papers in alphabetical order, and apparently he lost the two on the bottom.”

Professor Bottlebutt had his own way of dealing with exams.  He would grade them himself and work up the statistics for the class.  He would then hand back the papers to the class for a few minutes to allow the students to look them over.  Then he would put them into alphabetical order and give them to his assistant to record.

“If you tell me your correct scores, I will have my assistant record them,” he said.

Buster was astonished.  Dr. Bottlebutt was willing to take his word.  This was an opportunity for him to improve his grade.  He was straining through his brain for a number when he heard Betty’s voice from next to him.

“Ninety-eight,” she said.

Mesmerized by the sweet sound of her voice and not being the sharpest tool in the said, Buster followed suit.

“Yeah, me too, ninety-eight,” he said.,

The professor, who was sitting at his desk, glanced upward at both of them with a look on his face that was not indicative of credulity.

“Ninety-eight,” he echoed.

“Uh...,” Buster began but he didn’t get far.

“You know,” Bottlebutt said, “I don’t think that is exactly believable.  Let’s see.  The class average, which I calculated before your papers were lost, was about 70 and the standard deviation was about 6.  This means 98 is just over 4 standard deviations from the mean. That is unlikely for any population, but we have only 20 students in class.  By Chebyshev’s Rule, only 1 over 4 squared of the data can be that far from the average, that only 1 in sixteen. Now 20/16 is between 1 and 2.  So there is some chance that one of you can have that grade, mathematically speaking, but by Chebyshev’s it is mathematically impossible for both of you to have a grade that far from the average.”

Buster stood with his mouth open.  He noticed that Betty didn’t move a muscle. Not even her eyes moved.  Her chest was still moving in and out with a beautiful rhythm...

Butster looked down at the professor and noted that he was still staring up at them.

“Does either of you have anything more to say?”

Buster glanced Betty’s way and her expression was as innocent as a dove.  It made him ashamed of lying, but before he could own up, the professor continued.

“It might be well for you to know that since I’d figured up the statistics for the class  I was able to figure out some information from the rest of the papers,” he said. “The sum of your scores is 140.”

Buster thought of the score he’d really made, 70, and then, in spite of not being the sharpest tool in the shed, figured what Betty’s score had to be. She’d made 70 too.  Two thoughts raced to share his mind. One: They’d made the same score and had something in common.  Two: She was lying her gorgeously perfect backside off.

Buster looked at Betty.  The expression was so slight that he didn’t know whether it was there or whether he was imagining it.  It was in the eyes; it was around the curve of her beautiful lips. Please don’t give me away.

“Uh...Dr. Bottlebutt, did I say 98? I must have misspoke,” Buster said as he frantically tried to do mental arithmetic. “My real score is...”

“Forty-two?” the professor interrupted him.

Buster did a quick 98+42=140 and answered, “Uh...yeah.”

“There is a problem with that,” Dr. Bottlebutt said. “Forty-two is also more that four standard deviations from the average.  There can only be one that far away, high or low.  Do you want to stick with that?”

Buster looked at Betty, who was the most beautiful example of the human female that he’d stood in the presence of.  She was still holding that expression. It was so subtle, but so compelling.

“Yes,” he said, “sure.”

Bottlebutt looked up at both of them.

“You know,” he said, “I could take ten or twenty minutes and work this out. It’s not hard. I’ve got all the information I need.  But I think there is a learning opportunity to be had here, so I am going to take both of your words as true.  Good day.”

With that, they were dismissed.

Buster walked into the hall with Betty.

“Betty,” he began.  His next words were going to be about maybe going to get a latte or something, but no one was listen.

Betty walked over to the tallest, most broad shoulder man Buster had ever seen.  She put her arm around him and he put his hand in her back pocket. And the strolled away.

Buster, more than a bit crestfallen, got kind of a bitter taste in his throat. He turned and saw Bottlebutt who had clearly taken in the whole scene.

Buster stood there wordless and didn’t expect the professor to say anything, but he did.

“There are some lessons harder in the learning that math,” he said.