4 · Data Cleaning & Missing Data · Missing Data: Time Series & Diagnostics

Linear interpolation

Linear interpolation estimates a missing value between two observed points by assuming a straight-line change across the gap. It is common in ordered or time-indexed numeric data when short gaps are plausible.

Reference lessonPython exampleVisual explanation

Intuition first

What this concept means in practice

The practical value of Linear interpolation comes from understanding both the transformation and the boundary around it: what information is allowed to enter, what assumption is being made, and how you know the result is still valid after the transformation.

A beginner-friendly way to reason about it is to start with a tiny case where the correct result can be checked independently. Once the mechanism is clear, scale the exact same reasoning to larger tables, pipelines or models.

PurposeUse for short gaps in smoothly varying numeric sequences.

MechanismLocate the previous and next observed values and fill intermediate points proportionally to their relative position.

EvidenceInspect intermediate and final output; compare with an independent expectation.

Main cautionDo not bridge long gaps, abrupt regime changes or categorical variables as if they were linear.

Mechanism

Trace the operation from input to decision

Locate the previous and next observed values and fill intermediate points proportionally to their relative position.

1Input→

2Apply rule→

3Inspect state→

4Validate→

5Use result

Key rule

For a point fraction t between neighbours y0 and y1: y(t)=y0+t(y1-y0).

Visual explanation

Make the structure visible

The interactive view uses a concept-specific plot when the topic maps naturally to one; otherwise it uses a workflow view instead of leaving a broken placeholder.

Loading visual…

Practical example

Where you would use it

A temperature sensor records 20°C at 10:00 and 24°C at 10:20; the missing 10:10 value is interpolated to approximately 22°C.

Use when

Use for short gaps in smoothly varying numeric sequences.

Pitfall

What can make the result misleading

Watch out

Do not bridge long gaps, abrupt regime changes or categorical variables as if they were linear.

A useful diagnostic question is: Could the same code still run successfully if the analytical assumption were wrong? If yes, add an explicit validation check rather than relying on execution success.

Implementation

Miniature Python example

Keep the example small enough that you can inspect each stage manually.

Python

# Purpose: demonstrate Linear interpolation with a small, inspectable example.
# Follow the comments and printed stages to connect each operation with its result.
# Import the library or helper used in this example.
# Step 1 — Import the module so its functions/classes are available to the rest of this example.
import numpy as np
# Import the library or helper used in this example.
# Step 2 — Import the module so its functions/classes are available to the rest of this example.
import pandas as pd

# Create a small labelled dataset that is easy to inspect by eye.
# Step 3 — Compute the right-hand expression and store its result in `ts` for the next step.
ts = pd.Series([20.0, np.nan, np.nan, 26.0, 27.0, np.nan, 31.0, 32.0],
               # Store this intermediate value with a descriptive name for the next step.
               index=pd.date_range("2026-01-01", periods=8, freq="D"))
# Print this intermediate result so you can verify the workflow step by step.
# Step 4 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 1 · Missing values:", int(ts.isna().sum()))
# Store this intermediate value with a descriptive name for the next step.
# Step 5 — Compute the right-hand expression and store its result in `filled` for the next step.
filled = ts.interpolate(method="time", limit=2)
# Print this intermediate result so you can verify the workflow step by step.
# Step 6 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 2 · Missing after interpolation:", int(filled.isna().sum()))
# Print this intermediate result so you can verify the workflow step by step.
# Step 7 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 3 · Result:")
# Print this intermediate result so you can verify the workflow step by step.
# Step 8 — Display the current value explicitly so the result/state can be inspected during execution.
print(filled.round(2).to_string())

Expected / illustrative output

STEP 1 · Missing values: 3
STEP 2 · Missing after interpolation: 0
STEP 3 · Result:
2026-01-01    20.0
2026-01-02    22.0
2026-01-03    24.0
2026-01-04    26.0
2026-01-05    27.0
2026-01-06    29.0
2026-01-07    31.0
2026-01-08    32.0
Freq: D

Implementation checklist

Before you move on

Can you state what data or object enters the operation?
Can you explain what changes and what must remain invariant?
Have you checked the result on a tiny case you can verify independently?
Have you considered the main failure mode described above?
Can the operation be reproduced from code/formulas and documented assumptions?