u/Upper_Opening_4805

Just a few questions from a ninth-grader, about central tendency and spread

1. The program I'm using to learn math tells me that to find the variance, we divide the result of the sigma notation (\sum_{i=1}^{n}(x_{i}-x̄)^{2}) (paste that into desmos or some other equation displayer) by (n - 1) instead of by n for a more "reliable" result. Why does subtracting 1 from n make it a more reliable answer? I cannot think of any justification for subtracting 1 from n here.
2. To find the variance/standard deviation, we can't take the average of the distances between the values and the mean, since that just averages out to 0. But... why do we square (x_i - x̄) in the variance formula instead of just using the absolute value of (x_i - x̄)?? Would that not result in the average distance from the mean?
3. Why are the mean, median, and mode called measures of central tendency? Tendency, according to Merriam-Webster, is a "direction or approach toward a place, object, effect, or limit," which seems as though "central tendency" would mean the spread, not the center. The only possible solution I can think of is that these are the measures of which values the data in the list tends towards, but that just doesn't seem to fit very well.

1. Why can't we breathe in and out at the same time?

We could take in twice the oxygen with barely an increase in ATP use

Since we can already breathe in and out, AND have two holes for breathing (three if you count each nostril separately), it doesn't seem as though it would increase our demand on oxygen much

Like maybe an extra pair of lungs for exhaling

Edit: I realized two sets of lungs wouldn't work because one would inflate infinitely and the other would deflate infinitely, but larger lungs would serve the same purpose—the first comment taught me that birds do it with a complex sequence of inflating and deflating air sacs

And with double the endurance (less use of lactic acid) we could get double the food, so it's not like an extra organ system (and larger body to account for it) would have a shortage of glucose

2. Are there any organisms that can already do this?

3. Also, I know frogs drink through their skin; what if we could breathe through skin?

That seems like something even more beneficial (to my inexperienced eyes), since you're just taking in more air, and respiration isn't sharing space with eating

Look at my poem

It's quite a cool chess poem

It's a Hikaru

I've read TGED and Bountiful Harvest so far

Losing sight

The world becomes a vivid green
The seasons now have switched
As rain falls, it is slightly leaned
My gaze becomes bewitched
Then fog makes all the trees unseen
And color’s not as rich

Just Look Up

The pig can’t fathom eagles
It looks at solid ground
Until it gets eaten

What if I took a REALLY long stick and poked something with it? Could information be moved faster than light? Could I send almost instantaneous communications across giant distances?

Hypothetically, if I were strong enough to rotate the stick with its end as the pivot (bonus question: would it be possible to rotate the stick with technology?), would the other end move faster than light?

To what extent would I have to break physics to move this stick?