How do I compute the average difference in a list of numbers?

Question

I have a list of numbers:

 280,  449,  689, 959,  1360,  1740, 1139

Between 280 and 449, there is a distance of 169, and between 449 and 689, a distance of 240.

I need to know how in the simplest way that I can find the average numerical distance between these numbers.

Would I find the distance between each add them together and divided it by the number of items in the list?

Let me put it another way. If I have 3 numbers 1, 5, 8

there are 3 numbers between 1 and 5 and 2 numbers between 5 and 8

Let us say I want to put a number between 1 and 5, should that number be 2,3 or 4?

"average numerical distance" does not have a standard meaning as far as I know. Is there more context to this? — DavidButlerUofA, Jul 11 '14 at 03:21
because i need to fill in missing numbers between them so I want to calculate what to put between them — mcgrailm, Jul 11 '14 at 03:29
We're getting closer to the answer: what do you mean by "in between"? — DavidButlerUofA, Jul 11 '14 at 03:32
I am just trying to figure out what number should go between them if it should be 50% of the difference between each number or if there is a better solutions — mcgrailm, Jul 11 '14 at 03:54

score 3 · Accepted Answer · answered Jul 11 '14 at 05:00

I think what you are trying to do is put a number between each pair that is somehow halfway between them.

Therefore, for each pair of numbers, you should find the average of the two numbers. This is the number in between. For example, the number between 280 and 449 would be (280 + 449)/2 = 364.5, and the number between 449 and 689 would be (449 + 689)/2 = 569.

Other possibilities:

Method 2. Assume that the difference is approximately the same and calculate an average change from one step to the next from the first and last value. You have 5 steps and an overall difference of (1139 - 280) = 859. Dividing this by 5 steps gives 859/5 = 171.8 increase per step. You actually want half-steps, so each half-step would be 171.8/2 = 85.9. So the number between 280 and 449 should be 280 + 85.9 = 365.9 and the number between 449 and 689 should be 449+ 85.9 = 534.9.

Method 3. Use the above slope to draw a line of best fit for the data, and use the formula for this line of best fit to fill in the gaps. You want a line through the first and last point. We know this has slope 171.8 per step. At step 0, the value is 280, so the formula for the line is y = 280 + 171.8*step. The number between 280 and 449 is at step 0.5 so its value is 280 + 171.8*0.5 = 365.9; the number between 449 and 689 is at step 1.5 so its value is 280 + 171.8*1.5 = 537.7.

Method 4. Use proper regression to get a line of best fit for the data, with the x-values being the numbers from 0 to 6, and use the formula for the line of best fit to fill in the gaps. The slope and intercept for this regression are 208.21 and 320.5, so the formula is y = 320.5 + 208.21*step. The number between 280 and 449 is at step 0.5 so its value is 320.5 + 208.21*0.5 = 424.6 ; the number between 449 and 689 is at step 1.5 so its value is 320.5 + 208.21*1.5 = 632.8.

A graph showing these options is here: possible options

As you can see, method 1 seems to do what you want best (black dots are the original data).

Yes method one seems to be the best fit. I've learned quite a bit from this answer :D thank you for taking the time to explain this. And sorry I wasn't better at articulating what it is I wanted — mcgrailm, Jul 11 '14 at 11:01

user99680 · Answer 2 · 2014-07-11T03:55:52.400

2

Seems like: $$\frac{(L) - (S)}{ (T-1)}$$ would do it, where L is the largest value, S is the smallest value, and T is the total number of values.

edited Jul 11 '14 at 03:55

answered Jul 11 '14 at 03:36

user99680

6,708

hmm I don't think that is exactly what I want I ran this and got 394 as an average but if i put that between 449, 689 then that would not make sense since the number between them would have to be a number larger than the first and smaller than the second – mcgrailm Jul 11 '14 at 03:52
@mcgrailm: Sorry, that should be $T-1$ in the denominator. Let me edit. – user99680 Jul 11 '14 at 03:55
I'm unclear why - 1 ? – mcgrailm Jul 11 '14 at 03:57
Because there are $T-1$ "gas/spaces" between the T numbers in the list, i.e., there are a total $T-1$ numerical distances. – user99680 Jul 11 '14 at 03:59
Does that work better? – user99680 Jul 11 '14 at 04:00
ohh i got you lol I'm still not sure this is right did you see my first comment ? – mcgrailm Jul 11 '14 at 04:03
let me see it more carefully – user99680 Jul 11 '14 at 04:04
but you I almost always have numbers in the list that are both larger and smaller than the average, so the avg gap will not always work. – user99680 Jul 11 '14 at 04:15
ok so should I just split the difference between each set (halfway) – mcgrailm Jul 11 '14 at 04:21
yes, if I understood the question correctly. Sorry, I am not 100% I did. – user99680 Jul 11 '14 at 04:25
Sorry I could not be of more help. – user99680 Jul 11 '14 at 16:59
Thanks! This is exactly what I was looking for. – Nanoo Oct 22 '20 at 22:00

How do I compute the average difference in a list of numbers?

2 Answers2