Conan: The Mechanic

When all these things were happening in Tokyo, Okuki in the countryside was still calm, as if all this had nothing to do with the village.

After Chiba moved into the previously vacant house, the house gradually became lively. And, it wasn't just him alone.

Of course, Chiyu's current mind is not on these things, but sitting on the sofa in the living room, facing the homework book in front of her, in a daze.

[This confidence interval... How come what she wrote is different from the answer? 】

In the workbook in his hand, the process of a whole math question is listed in the answering area in beautiful small print, which makes anyone who reads it feel extremely pleasing to the eye——

If she answered correctly.

Gently frowning, Qianyu traced back the content of the answer from the bottom up, and quickly discovered the problem. "Ah... Sure enough, something went wrong here?"

Just when he discovered the problem, footsteps as light as a cat extended towards him from the direction of the kitchen.

"Qianyu," said the apron-wearing celestial girl Meoying with a smile. "Dinner will be ready soon! Have you finished your homework check here?"

"Yeah," Qianyu nodded. "Generally speaking, there is no problem...but you made a mistake in the sample variance, and you need to correct it later."

"Sample variance?" After thinking about it, Tiannv Muying seemed to remember the topic. "Ah, is that the confidence interval question?"

"Yes," Chiyu gently closed the workbook and stood up. "The sample variance is not the same as the population variance... The population variance is the sum of squares of the total deviation divided by N, and the sample variance is divided by (N-1), and if it is divided by N, the sample variance S2 will be biased. Underestimates the overall variance."

"Uh, it sounds very complicated..." Tiannv Muying's face immediately stiffened. "That...that...how about we finish dinner before we study?"

"..." Qian Yu looked at Ying's embarrassed look, and finally nodded with a chuckle. "Okay, okay, anyway, this is probably not something that can be told to you in a few minutes, let's eat first."

Although Ying usually lives alone, but because she lives in a shrine on the mountain, it is a laborious thing to buy ingredients to cook at home, so Chiba didn't have any confidence in Ying's cooking skills. But unexpectedly, the food she cooked tasted good.

"Although I do not often cook at home, I have a lot of cooking experience!" Ying explained to Qianyu. "Sister Baxun, as well as the grandparents in the village, often invite me to cook and eat with them, so I naturally practiced."

In other words, Chiba and Ying have formed such a life relationship - Ying will often visit Chiba's house when she has time to cook and share a more interesting tradition than the modern Western-style meals Chiba is familiar with or Local specialty food. And in return for that...

"But, why should the sample variance be divided by (n-1) instead of n?" Tiannv Muying sat beside Qianyu obediently and asked with a pen. "Isn't the population variance just n?"

"This question..." Qian Yu thought for a while. "Simply put, because the sample mean is an unbiased estimator of the population value, it is not consistent all the time... This difference will result in a sample variance equal to (n-1) times sigma^2, if you need to I can write a derivation for you. But if I remember correctly, this knowledge should not require you to master the specifics..."

"Then let's talk about it," the goddess Muying nodded. "Anyway...that's the only problem to be solved today, right? I can go back later, so it's better to fully understand this kind of problem."

So, what seemed to be simple in Chiba, but in the end, the painfully long teaching began.

"The variance of the sample mean is the individual variance divided by N. You can find out by calculating it with the formula."

"The sum here is not 0, the sum of these y's is n*sample mean rather than n*population mean, so it can't be eliminated here."

"It can be changed to sigma^2 because the expected value of the squared deviation is constant. Although not every squared deviation is this number, what we want to give is an unbiased estimator, not an accurate value. So it's translatable here -- don't confuse exact calculations and unbiased estimates, the former is impossible."

……

Chiyu breathed a sigh of relief after seeing that the celestial maiden Muying had written the derivation of the last line of the formula correctly.

"Congratulations... Now, you should have mastered this completely."

"Yeah, it's so complicated," Ying looked at the scraps of paper she had just used up, and showed a somewhat awkward smile. "My brain is really a bit stupid. Qianyu, what you have grasped so long ago, I have spent so much time."

"No, that's not really..." Qian Yu originally planned to comfort the goddess Muying, but she didn't know how to speak. "Anyway... this thing is a little out of line for you guys..."

When his words paused for a while, the sound of raindrops beating suddenly came from the windowpane not far away.

"Is it raining?" Ying Ru woke up from a dream and looked at the window, as if remembering something. "Ah! What time is it?"

Before Qianyu could report the time, she had already seen the time on the wall clock~www.readwn.com~9:50...Is it so late? "

"What's wrong?" Qianyu didn't react.

"I forgot to feed [Master]!" The goddess Muying looked a little uneasy. "Feed him this morning and he should be hungry again now."

[Master] is the cat that the goddess Muying kept in the shrine. When Chiba visited her house before, she often played with it, so she was quite familiar with it.

"Then..." Looking at the darkness outside the window, Qian Yu felt a little uneasy. "How about I take you back?"

The shrine where Tiannv Meei lives is located on a mountain, and it takes a winding mountain road to reach it. If it is said to be walking at night, it is actually quite dangerous.

"No, no need." The goddess Muying refused Qianyu's request without any hesitation. "It's not raining heavily this time, and I'm familiar with the mountain road back home - don't worry. And if you send me back, you'll have to walk back then, which is a waste of time."

"That's right..." Chiyu, who was rejected, felt a little down, but just nodded. "Then... well, pay attention to safety."

"Don't worry," the goddess Muying nodded with a smile. "It's just a light rain. It's safe on my way back, don't worry~"

Although she was a little uneasy, Chiyu could only reluctantly nodded. "Then...you pay attention to safety. Although you are familiar with it, it is indeed dark and the mountain road is slippery."

"Don't worry--actually, if you go back with me, you might end up being the one who doesn't quite adapt to the road conditions!" The goddess Muying was joking with Qianyu as she packed up her books. "So, don't worry about me, I'm very flexible!"