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Completely New Math Corollary

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Kane Jiang
Posts: 42
Joined: August 8th, 2019, 5:28 am

Completely New Math Corollary

Here is a completely new math corollary I invented.

For any mathematical average, the sum of how much larger than the average the numbers above are must equal the sum of how much smaller than the average the numbers below are.

Mathematical averages are usually calculated by adding all the numbers up and dividing the sum by how many numbers there are. The mathematical average of a group of numbers indicates the number overall the overall group is closest to.

Now an example of the corollary:

For example, if the numbers are 75 and 79, the average is 77 because 79 is 2 larger than 77 and 75 is 2 smaller than 77. This is common sense.

But what if you have 3 numbers? Let's say you have 74, 78, and 79. The average is 77 because 78 is 1 larger than 77 and 79 is 2 larger than 77 and 2 + 1 = 3. 74 is 3 smaller than 77 so 3=3. You can use guess and check until you arrive at the average if you're not sure which number to pick.

This method can help you calculate means of numbers that are close together faster in your head without adding up the numbers or the one's digits of the numbers. It will work on any mean.

Derivation of the corollary:
(Sum of n) / x = y
x is the number of numbers, y is the mean
Sum of n = x * y
Sum of n - x * y = 0
(Sum of n) /x - y = 0
(N1/x - y) + (N2/x - y) + ... = 0
Now put all the numbers below on one side and all the numbers above on the other side...
and that is a fail; maybe it's really a postulate instead?

2nd attempt
N1 - y + N3 - y = y - N2
N1 + N3 + N2 = 3y
(N1 + N3 + N2)/3 = y
If anything, the mean formula is derived from my corollary.

I'm not sure right now if it's a postulate or corollary, but I think it's a postulate and the common mean formula is a corollary to the postulate.

I'll get back to you on that one. In the meanwhile, feel free to post.

Copyright 2019 by Yukang Jiang

h_k_s
Posts: 777
Joined: November 25th, 2018, 12:09 pm
Favorite Philosopher: Aristotle
Location: Rocky Mountains

Re: Completely New Math Corollary

Kane Jiang wrote:
August 9th, 2019, 4:36 pm
Here is a completely new math corollary I invented.

For any mathematical average, the sum of how much larger than the average the numbers above are must equal the sum of how much smaller than the average the numbers below are.

Mathematical averages are usually calculated by adding all the numbers up and dividing the sum by how many numbers there are. The mathematical average of a group of numbers indicates the number overall the overall group is closest to.

Now an example of the corollary:

For example, if the numbers are 75 and 79, the average is 77 because 79 is 2 larger than 77 and 75 is 2 smaller than 77. This is common sense.

But what if you have 3 numbers? Let's say you have 74, 78, and 79. The average is 77 because 78 is 1 larger than 77 and 79 is 2 larger than 77 and 2 + 1 = 3. 74 is 3 smaller than 77 so 3=3. You can use guess and check until you arrive at the average if you're not sure which number to pick.

This method can help you calculate means of numbers that are close together faster in your head without adding up the numbers or the one's digits of the numbers. It will work on any mean.

Derivation of the corollary:
(Sum of n) / x = y
x is the number of numbers, y is the mean
Sum of n = x * y
Sum of n - x * y = 0
(Sum of n) /x - y = 0
(N1/x - y) + (N2/x - y) + ... = 0
Now put all the numbers below on one side and all the numbers above on the other side...
and that is a fail; maybe it's really a postulate instead?

2nd attempt
N1 - y + N3 - y = y - N2
N1 + N3 + N2 = 3y
(N1 + N3 + N2)/3 = y
If anything, the mean formula is derived from my corollary.

I'm not sure right now if it's a postulate or corollary, but I think it's a postulate and the common mean formula is a corollary to the postulate.

I'll get back to you on that one. In the meanwhile, feel free to post.

Copyright 2019 by Yukang Jiang
I think you will love Statistics when you get to college.

Statistics already has concepts of the mean, the median, and the mode, together with standard deviations from the same.

It sounds like you have discovered the standard deviation on your own in a different way.

Kane Jiang
Posts: 42
Joined: August 8th, 2019, 5:28 am

Re: Completely New Math Corollary

h_k_s wrote:I think you will love Statistics when you get to college.

Statistics already has concepts of the mean, the median, and the mode, together with standard deviations from the same.

It sounds like you have discovered the standard deviation on your own in a different way.

Well, I already have a bachelor's degree and I discovered this formula when I was in middle or high school, although I didn't tell anyone.

It would be useful on the SAT's, especially when you have multiple choice answers so you wouldn't even need to guess and check?
I've never heard of it being used on the SAT, so I'm pretty sure it's original and that's why I posted it here.

Kane Jiang
Posts: 42
Joined: August 8th, 2019, 5:28 am

Re: Completely New Math Corollary

h_k_s wrote:I think you will love Statistics when you get to college.

Statistics already has concepts of the mean, the median, and the mode, together with standard deviations from the same.

It sounds like you have discovered the standard deviation on your own in a different way.
Well, I already have a bachelor's degree and I discovered this formula when I was in middle or high school, although I didn't tell anyone.

It would be useful on the SAT's, especially when you have multiple choice answers so you wouldn't even need to guess and check?
I've never heard of it being used on the SAT, so I'm pretty sure it's original and that's why I posted it here.

h_k_s
Posts: 777
Joined: November 25th, 2018, 12:09 pm
Favorite Philosopher: Aristotle
Location: Rocky Mountains

Re: Completely New Math Corollary

Kane Jiang wrote:
August 13th, 2019, 3:17 pm
h_k_s wrote:I think you will love Statistics when you get to college.

Statistics already has concepts of the mean, the median, and the mode, together with standard deviations from the same.

It sounds like you have discovered the standard deviation on your own in a different way.
Well, I already have a bachelor's degree and I discovered this formula when I was in middle or high school, although I didn't tell anyone.

It would be useful on the SAT's, especially when you have multiple choice answers so you wouldn't even need to guess and check?
I've never heard of it being used on the SAT, so I'm pretty sure it's original and that's why I posted it here.
Did you take any Statistics courses while in college? Your algorithm sounds exactly like the "standard deviation" function in Stats.

Kane Jiang
Posts: 42
Joined: August 8th, 2019, 5:28 am

Re: Completely New Math Corollary

What standard deviation function? I did take a stats course but my algorithm was devised before I took the course. Can you tell me what formula you’re referring to?

Kane Jiang
Posts: 42
Joined: August 8th, 2019, 5:28 am

Re: Completely New Math Corollary

h_k_s wrote:Your algorithm sounds exactly like the "standard deviation" function in Stats.
If you mean this formula sqrt(sum of (x - mean))^2/n), I don't think that formula has any correlation with my algorithm. For one, I also use mean - x in my algorithm and there are no square roots or exponents. I also don't divide by anything?