Interpolation
Interpolation is a Grade 7 math skill from Yoshiwara Intermediate Algebra used to estimate values within a known data range. By finding a linear or quadratic model that fits the data, students can predict y-values for x-values that lie between observed data points.
Key Concepts
Property Using a regression line to estimate values between known data points is called interpolation .
Examples Cocoa sales data is collected for temperatures between $2^\circ$C and $18^\circ$C. Using the regression line $C = 2.5T + 52$ to predict sales at $9^\circ$C is interpolation. We get $C = 2.5(9) + 52 = 29.5$ cups.
A baby whale's length is recorded at birth (0 months) and 7 months. Using a linear model to estimate its length at 4 months is interpolation, because 4 is between 0 and 7.
Common Questions
What is interpolation in mathematics?
Interpolation is the process of estimating unknown values that fall between known data points using a mathematical model such as a line or curve.
How is interpolation different from extrapolation?
Interpolation estimates values within the range of known data, while extrapolation predicts values outside the range. Interpolation is generally more reliable.
How do you perform linear interpolation?
Find the equation of the line through the two nearest data points, then substitute the desired x-value to estimate the corresponding y-value.
When is interpolation used in real life?
Interpolation is used in weather forecasting, engineering measurements, scientific data analysis, and any situation where exact data is unavailable for a specific value.