How do I interpolate?

Question

I have a range of 20 points ranging from 20 to 40 20 = 4 and 40 = 7, what does 26 equal and how did you do it, so I can remember how to interpolate.

Answer 1

Assuming it is a linear interpolation, you can graph the two points, draw a line and then figure out what x = 26 will give you for y...

You can also do it mathematically by figuring the equation of the line. You have a rise of 3 (subtract y-coordinates, 7-4) and a run of 20 (subtract x coordinates, 40-20). So the slope is 3/20.

Next you have to figure out where it will intersect the y-axis. That's the point where x = 0. We already know that for every 20 points (in x) there's a change of 3 (in y), so going backwards 20 points, there would be a drop of 3 points. In other words, going back from (20,4) you get to (0,1). So the y-intercept is 1.

Putting this into slope-intercept form (y = mx + b) you have:
y = (3/20)x + 1

Double check by putting in x = 20 and x = 40, you should get y = 4 and y = 7.

Now just plug in x = 26 and see what you get for y:
y = (3/20)26 + 1
y = 78/20 + 1
y = 3.9 + 1
y = 4.9

And that is your answer using linear interpolation. For the point 26, you would get 4.9.

Another way to do it is to just use just the slope. You know the slope is 3/20.
From 20 to 26 is 6 points.
6 x 3/20 = 9/10 = 0.9.

This means that at 26, it will be 0.9 more than at 20.
So adding 4 + 0.9 you get 4.9, just like before.

For the point 26, you would get 4.9.

Answer 2

Interpolation

The process of inserting additional words in a complete document or instrument in such manner as to alter its intended meaning; the addition of words to a complete document or instrument.

Interpolation is synonymous with interlineation.