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