Interpolation (noun)

1. The act or process of inserting or introducing something between other things or parts.
2. The calculation of a value between two known values in a sequence or table of values.

Origin:

Late latin interpolatio, from latin interpolare to renew, restore, from inter- + polare to polish, restore.

Examples:

1. The singer's interpolation of a few lines from a different song was met with cheers from the audience.
2. The interpolation of the missing data allowed the researchers to complete their analysis.
3. The scientist used interpolation to estimate the temperature at the surface of the planet.
4. The interpolation of new notes between the existing ones improved the melody.
5. The interpolation of a new scene into the movie required reshoots and special effects.