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[Naturegirl1999]

How I got the number I did was googling swallow flight speed, which gave the result of 31-40, then I added 31+32+33+34+35+36+37+38+39+40, then divided the result by 10 (number of numbers within the adding process))

[ChairmanPoo]

Yeah but is that an African swallow or an European swallow?

[Naturegirl1999]

It did not specify, apparently the speed given is the average of multiple species called swallows

[Reelya]

How I got the number I did was googling swallow flight speed, which gave the result of 31-40, then I added 31+32+33+34+35+36+37+38+39+40, then divided the result by 10 (number of numbers within the adding process))

You do know that if you have a range, all you need to do is add the lowest and highest number and divide by 2? You get the same answer.

[wierd]

ONLY IF DISTRIBUTION IS NORMAL!!

[Reelya]

You can't really say "only" if it's normal. It's still true if it's linear. For example the average roll of 1 die is 3.5 : (1+6)/2 and dies are not normally distributed, but this still works. What you mean is symmetric or something.

But the point was that she was adding up all 10 numbers then dividing by 10. You always get the same answer by adding just the top and bottom and halving them in that situation.

[wierd]

*resists urge to verify hunch of a violating case*

(Just a hunch-- but say you have a pattern of decimal fractions included, say, between 1 and 10, but also adding a linearly increasing but irrational portionality. Say [1 + 1.333 + 2.666 + 3.999 +4(+1.222) +5(+1.555) +6(+1.888) +7(+2.111)....] )

*gives in, test it*

The hunch string, carried out to 10 (+linear attache), added together, then divided by 10, gives an average of 7.2999(...)
Taking the top and bottom, adding together, and dividing by 2, gives 7.

[Egan_BW]

neeeeeeeeeerds <3

[Reelya]

snip

That's entirely besides the point. I was just pointing out a quicker way to do the same calculation NG did. That an entirely different calculation gives a different answer is irrelevant. The midpoint is just the highest plus lowest divided by 2, you don't need to sum all the points in between and divide by the number of points.

Similarly a question could ask you to add all the numbers from 1 to 100, and you could do that manually, or you could apply the formula for it : n(n+1)/2 for n=100. It's an entire non-sequitur to then come along and state that 33.75 is technically a number between 1 and 100, therefore the formula is wrong, because it's entirely missing the point / being obtuse.

EDIT, however the pascal formula suggests an even better way to solve the problem. Calculate the pascal number for 40 (which is the sum from 1 to 40), subtract the pascal number for 30 (which is the sum from 1 to 30), then divide by 10. So we have the much handier formula of (40*41/2 - 30*31/2) / 10 for the speed of the swallow. And that still uses less computations than adding all the numbers together

[wierd]

No no no--

The string I gave is a fixed linearly increasing proportionality.

Specifically, "Next N = N + 1+ (1/3)"


Your sample one is "Next N = N + 1"

[Reelya]

Like i said, you're entirely missing the point on purpose obviously.

I simplified the formula she provided. That you can pull some random unrelated formula out of your ass and it'd different isn't in fact a trick.

The fact that your solution gives a different answer to NG's makes it invalid, it's not a valid simplification of the math she provided.

[wierd]

One of us is I think.

Your argument was literally "It's still true if it's linear".
(So, I provided a linear expression that disproves that.)

The real breaker, is when there is an asymmetry across the midpoint.

[Reelya]

Well your math is wrong then.

If you have a linear set of numbers, equally spaced, and they start at one point, and end at another, then summing the highest and lowest and dividing by how many points always gives the midpoint. As does summing all the points and dividing by the number of points.

The problem is that the distribution you gave is not in fact linear, because the spacing between consecutive terms is not the same.

It's not me, it's maths:
https://www.onlinemathlearning.com/linear-sequences.html

What is a sequence?
A sequence is a list of numbers that follow a pattern.

What is a linear sequence?
A linear sequence is a list of numbers that increases or decreases by the same amount each time.

So, NG's one was a linear sequence with a step size of '1'. But you can calculate the sequence with different linear step sizes. As long as the start and end points are the same, the average value will always be the same (midpoint).

[wierd]

I think you might be right on it not being linear..  (this is why I do so many battles with the bad idea generator in my head.)   I think I made it discretely exponential, since it continually accumulates 1/3rds, rather than blandly adding 1/3rds.

But meh- the real dealbreaker is still when there is asymmetry over the midpoint.  If the distribution is not uniform on both sides of the period, the trick will fail.

[Reelya]

You've clearly made a mistake, because that's not how numbers work. either you broke math and you're a genius, or you did a typo.

Or you don't understand the different between a linear sequence and a geometric progression or similar. Linear means linear, it means a constant step size, not an "accumulating" step size.

The easy way to see why it's true is that if you have 'n' points and you graph them on a 2D plot, with the points numbered along the bottom, then you get a straight line. Hence, linear sequence.