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One rainy day in school, three friends were gathered in the classroom of Sir Holtzman along with more than 30 students. The three friends’ names were Yates, Gilbert, and Tolan. Their topic that day was about measurement.
“Okay, class, so what do you know about accuracy?” Sir Holtzman asked.
Tolan raised his hand, and when he was called, he stood up and said, “Accuracy is the closeness of the given value or values to the true value.”
“Okay, and what about precision?” Sir Holtzman asked.
Gilbert raised his hand and said, “Precision is the closeness of the given values to one another even though they are not close to the true value.”
“Exactly!” Sir Holtzman exclaimed. He went further to discuss the meanings of the two terms, then said, “All right, now that we know the meaning of accuracy and precision, let us proceed to computing values. For accuracy, we compute for the absolute error and the relative error. For precision, we get the absolute deviation and the relative deviation.”
His eyes slowly glanced at each of the students, then landed on a boy who was apparently busy tapping away on his phone, obviously not interested with the lesson. “Yates, since you’re so busy with your phone, can you read to us the definition of absolute error shown in the PowerPoint presentation?”
Yates rolled his eyes and gave his phone to his teacher before reading, “Absolute error is the actual difference between the measured values and the accepted value.”
Sir Holtzman tucked Yates’s phone in his pocket, mentally taking note to return it later, and started to explain the procedure in computing for the absolute error.
“To get the absolute error, you just get the difference of the observed or measured value and the accepted or the true value. Take note of the two bars in between; that means we need to get the absolute value of the difference, meaning the final answer will always be positive,” he smoothly said.
“Ashton, can you try and solve for the absolute error if the measured value is 13.9 cm and the accepted value is 14.2 cm, then kindly explain how you got that answer?” Sir Holtzman called to one student seated at the back.
The student, Ashton, nodded and smiled before standing up and going to the board to answer the question. He quickly finished solving the problem and faced his teacher and his classmates.
“The answer for this problem is 0.3, since when you subtract 14.2 from 13.9, the answer is actually negative 0.3. But since we need to get the absolute value, negative 0.3 becomes positive 0.3,” Ashton smoothly explained.
“Correct!” Sir Holtzman grinned, happy with Ashton’s confidence and performance.
“So, moving on. For the relative error, you divide the absolute error by the accepted value, then multiply their quotient by 100. Never forget, class, to always add the percent sign (%) when getting the relative error,” he firmly told his students.
When done with accuracy, they moved on to computing for the precision. “Okay, class. For the precision, we get the absolute deviation and the relative deviation. Don’t be confused! In accuracy, it is the ERROR we are looking for, while in precision, it is the DEVIATION,” Sir Holtzman clarified to his students.
He continued, “To get the absolute deviation, you just subtract the means of several readings or the average of the measured values to the given measured value. Then for the relative deviation, you divide the average of the absolute deviation, divide it by the means of several readings, then multiply it by 100. And like with the relative error, you always include the percent (%) sign. Got it?”
The students nodded in understanding, and Sir Holtzman gave a few exercises to see if they really understood the lesson.
Later that day, when the three friends were gathered in Tolan’s house, they were studying for their prelims the following week.
“I have to admit that the lesson today in Physics was easy,” Gilbert remarked while reading over his notes from today’s class.
Tolan, who sat beside him, nodded, but Yates said, “But he still fucking confiscated my phone.” He laid on the couch and pouted, making his best friends chuckle.
“Mate, you were practically shoving your phone in his face. And he specifically told us during our first day that phones weren’t allowed,” Tolan said.
Yates suddenly sat up and looked at his two friends, a deep thought suddenly forming in his mind. “You know, I realized something important related to measurement or accuracy or whatever our topic was earlier.”
Tolan and Gilbert were intrigued by Yates’s sudden bright tone, so they listened to him intently. “Computing for the accuracy and precision, or measurement in general, is like solving problems in life. It’s all trial and error. You just keep trying and trying until you get the right solution or the correct answer. It’s the same with life. You try and try---”
“Until you die?” Gilbert interrupted, making Tolan giggle, but when Yates glared at them, they kept quiet, making him continue.
“You try and try until you get the answer you’ve been looking for. It’s like a cycle that you choose not to give up on until you’re satisfied with the result.”
Tolan and Gilbert shared a look of amusement before clapping and tackling their friend in a hug.
“Where the hell did you get that from? That was so deep,” Gilbert commented.
“It’s a great comparison, Yates. I never expected that from you,” Tolan teased as he ruffled Yates’s hair.
Yates rolled his eyes fondly at his friends and shrugged. “I don’t know, it came out naturally, I guess?” Gilbert and Tolan tackled him once again, making the three of them laugh.
They finished reviewing that night, and before they went to sleep, for the first time, they felt confident about their exams.