# How Data Points Build Up

This silly SVG animation (animation not my strong suit) demonstrates what happens when multiple Tgres data points arrive within the same step (i.e. smallest time interval for this series, also known as PDP, primary data point).

### Explanation

Let’s say we have a series with a step of 100 seconds. We receive the following data points, all within the 100 second interval of a single step:

Time Value Recorded
25s 2.0 0.5
75s 3.0 2.0
100s 1.0 2.25
Final: 2.25

Tgres will store 2.25 as the final value for this step. So how does 1, 2 and 3 add up to 2.25?

One way to think about it is that the incomplete step is an empty swimming pool as wide as 1 step, into which we dump blocks of water. The first data point dumps a 2.0 × 0.25 block of water, which fills the pool to 0.5. The second data point dumps a 3.0 × 0.50 block, which raises the water another 1.5 to 2.0. The last data point dumps a 1.0 × 0.25 block which raises it to the final value of 2.25. Compare this with Graphite which would simply discard the first two data points and we are left with 1.0 as the final value.

Why is it done this way? Because this is how rates add up. If this was speed of a car in meters per second (more like a bycicle, I guess), its weighted average speed for the duration of this step of 2.25 meters per second would mean that in the 100s it would have traveled exactly 225 meters.

### NaNs or “Unknowns”

What if instead of the first data point, the first 25s were “unknown” (recorded as NaN)? This would happen, for example, if the series heartbeat (maximum duration without any data) was exceeded. Even though the data point has a value of 2.0, it gets recorded as NaN.

Time Value Recorded
25s 2.0 NaN
75s 3.0 2.0
100s 1.0 2.33
Final: 2.33

But wait a second… 0.50 × 3 + 0.25 × 1 = 1.75 ? Where did the value of 2.33 come from?

The reason for this is that NaN ought not be influencing the value. The above calculation would only be correct if we assumed that NaN is synonymous with zero, but that would be a false assumption, as NaN means “we do not know”.

Therefore, we must only consider the known part of the data point, which is 75s. We can think of it that the data point (the “swimming pool”) just got smaller. Thus the correct calculation for the 3.0 point would be 3.0 × 50 ÷ 75 = 2.0 and for the 1.0 point 2.0 + 1.0 × 25 ÷ 75 = 2.33.

Here it is in SVG:

Also note how the value of the data point which was recorded as NaN (2.0 in our example) is essentially irrelevant. This is because any calculation with a NaN always results in a NaN. The only thing we know about this data point is that it was not NaN and that it marked the end of period recorded as NaN. The next data point after this (3.0 in our example) is not affected by the NaN, however, this is because it in effect starts its own data point afresh, not considering anything in the past.